professor Steven Patel who's delivering a faculty seminar for us today. Steven's about to become full professor at the University of Western Ontario but a loyal alumnus of Dalhousie Law School as it then was and take it away Steven. Do you want to trade seats now? No, this is okay. I think as long as we're good and set up for the recording. Brent, thanks very much. Richard, thank you very much for hosting and for organizing. I know time is difficult and I want to thank everybody for attending because a tough time of the week and of the day so I'm grateful for the opportunity to have an audience to talk about this issue. I want to thank especially given that we're recording for posterity I want to thank obviously my co-author Jordan McKee who is a second-year student at Western University at the moment so this was a project that he worked with me on in his summer after first year and it's very good work for somebody at that stage of their legal education and I want to thank the law firm of Goodman's LLP which sponsors the Goodman's faculty fellowship in legal ethics and professionalism at Western University and has allowed my colleague and co-holder of the fellowship Randall Graham and I the opportunity to do some interesting things in the legal ethics area but for the funding that we receive might not otherwise have been possible so I'm quite grateful for that. I understand from Richard that the audience has or at least has had available an earlier version of this paper. This paper sort of been a work in progress and I looked at it and got it to a particular point last fall and over the course of the last week or so in preparing for this particular discussion it's evolved I think in some ways significantly so I'm warning you now in advance of those of you that might ask questions about specific things that the paper you have in front of you says my answer may well be doesn't say that anymore that's now gone and it says something different so that may be my strategic outlook although the theme of the paper and the ground that the paper covers certainly hasn't changed but the way some of the arguments are put I think has been made a bit more focused and a bit clearer. So the topic which I will introduce just by way of setting out a sort of standard fact to get out in front or lay some groundwork for an area that I think become a more involved area over time and I suppose the third reason I think the paper is of value is in a sense it's applying a number of Canadian ethical principles from some of the key leading cases and from some of the rules that we have to a particular situation as a kind of a case study and even if the case study may not be all that commonly arising out there in practice we can still learn a number of things about the rules themselves from seeing how they apply to this particular case study. So the scenario that the paper talks about is this we have a client who hires a law firm and we're going to talk mainly about major large law firms hundreds of lawyers at a law firm typically. Client hires a law firm there's a partner on the file who's primarily handling the file and maybe other lawyers in the firm who are working on the client's matter and something happens that leads the partner to think we may have violated some ethical obligation here in handling the client's matter or we may have committed malpractice we may have actually done something wrong as lawyers in handling this this file for the client. So the partner goes down the hall to another lawyer in the firm and says look here's the problem here's what's happened you're an experienced person you know a lot about malpractice and legal ethics and that sort of thing what should we do in order to minimize or reduce our exposure and protect ourselves as a firm and how do we make this problem go away and maybe be able to satisfy our concerns and the client's potential concerns and keep this thing moving forward and so there's there's a communication there there's a discussion there there's correspondence perhaps back and forth between the partner and that other lawyer within the firm something it's written documented what have you partner makes a decision and partner based on that carries on with acting on the client's matter and even that could take a number of forms that that could take a number of forms in terms of the lawyer just saying to the client oh by the way I looked into this and we're we're good to go it's not a problem I've satisfied ourselves that there's no no difficulties here so not something you'd even thought of client but I'm I thought about it and we're fine and away we go at a much more dramatic end of the scale it could be actually having to tell the client we think we may well have screwed up here we think there may be a problem involving our malpractice and we're now getting into much more difficult conversations with you client about you potentially having to go refer find new counsel and potentially have to think about having a claim against us as a firm based on our our malpractice so there's a wide spectrum of kind of what could happen when the partner lawyer goes back and talks to the client after this this circumstance what the firm is likely to want to happen though is somehow that the matter continues on that the firm continues acting for the client they've sort of smoothed over whatever the problem was and that they carry on so let's say in one of those lesser cases where the firm hasn't sort of directly come out and told the client this has got to come to an end you're gonna have to go ahead and get new counsel the client starts being concerned the client says ooh I hadn't thought of that are you sure we're okay and can you fill me in more and why we're okay and in fact could I see what this other lawyer told you or wrote down for you as to why it is you now think you're okay or the client might say oh I'm pretty sure we're not okay this sounds horrible and the client decides to pull the plug and go retain new counsel and sue the former lawyers for malpractice and in any number of those situations the issue then that I'm focusing on is what happens if the client says I want to see the communication between you partner and the lawyer you went to talk to you within the firm about this issue I want disclosure of that I want you to give me a copy of that communication passing between you within the firm and at one level we might think that should just be a no-brainer I'm the client I hired this law firm that means I hired all the lawyers at this law firm for work for me there can't possibly be anything passing between those lawyers in the firm about my case that they can keep from me I'm the client they owe me a fiduciary duty they owe me a duty of candor they got a release whatever they've got that relates to my my matter and what the paper does is it suggests and maybe we can think about that differently there might be a different answer to that question that it might actually be possible and that's what the paper wants to explore that the firm could claim privilege that the firm could actually claim a solicitor client privilege for the communication passing between what we're called the ethics council within the firm and the partner who went to get the advice from the ethics council and that the firm could set that privilege up as against its client and say you don't get to see what we were told because that was legal advice provided to us and so it's privileged and you don't get to see it you don't get to see it by requesting it and you don't get to see it through a discovery process if you're suing us for malpractice and so what what the paper focuses on is could that work I mean could such a claim for privilege be entertained would it be successful and if conceptually it could work what are the circumstances in which we think it it viably could work or should work in other words what preconditions might what what what might we need to add to that fact situation that I've set out before we would think that privilege could attach to that communication so the paper then divides into after setting that up the paper divides into into two parts and the first is to look at the American experience on this issue because I didn't just wake up one day and think hey what a neat idea I became aware that this is an issue in the United States that there are cases on this issue and that there is some jurisprudence on this issue and some writing on this issue commentary on the issue and so I wanted to explore what the American experience is on this question and I wanted to see how could that potentially translate over into the Canadian context and so the first part of the paper deals with the American experience and it's much longer than I would like it to be for an article that's primarily aimed at mapping the issue for a Canadian landscape and but the reason it's long longer than I would sort of like it to be is because there isn't a useful summary of the analysis of the American law out there in the American literature and the law in the US is in flux so over literally the last two years there have been some fairly significant developments in the US case law on the issue that haven't translated into an easy reference point that I could just take on board as a starting point for the US law and and go from there so I needed in the paper to map out the position in the United States before then seeing where that would take us in in Canada so that's the way I'll divide up the remainder of the time that I have is to say a little bit about the American context and then to look at more perhaps at the Canadian context so in the US the short answer is yes there is such privilege you can claim privilege on communications between a lawyer and a firm and their ethics council uh the reason that that then gets very problematic is because and and they got to that position not perhaps surprisingly by analogy with in-house counsel and at a corporation right so in other words if a corporate if any other large entity like an accountant firm or a bank is allowed to have in-house counsel why shouldn't law firms be able to have in-house counsel and if privilege attaches to communications within house counsel generally why shouldn't privilege attach to in-house counsel or happen to be in-house within a law firm so the Americans said that that should be fine there's no real conceptual problem there the problem is literally almost in the same breath as saying that the American jurisprudence said but the privilege will always be defeated if in-house counsel is in a conflict of interest vis-a-vis the the sort of the client the original client and the firm and that I guess that's how we might pull back for a second and say well why should a conflict of interest defeat the operation of a privilege but he maybe even setting that to one side I we can certainly see that we would be concerned if there was a true conflict of interest between the in-house counsel and the original client and and the firm and that that might well cause us pause to as to allowing a privilege to operate with regards to these communications but the problem is the American jurisprudence then said well if the client the original client is a current client the part the original partner has an obvious conflict of interest because they know about the clients the need to put the clients interest first and all the rest of it but they also now are on notice that the firm may have a separate and divergent concern from the client's concern being sued for malpractice having done something wrong ethically oh and by the way says the American law that conflict is automatically imputed to every other lawyer in the firm including in house ethics council so going down the hall to the ethics council doesn't solve the problem that's no different than you just asking yourself in your office how to handle this dimension so the American law says yeah the privilege exists but in paradoxically the case where you would most need it to operate which is while the client is still your client you're in a conflict of interest that you can't get out of and therefore that defeats the privilege and that's to be distinguished from the situation where somehow if you fire the client or the client bails on your firm and then you go to your in-house council and start preparing a defense for example that's privilege no no no problem again in the American law that that's privileged because they're not your client anymore so you don't have a conflict of interest there okay but that's not controversial and that shouldn't trouble us right the difficulty is law firms are likely going to need to get legal advice before their client has bailed on them either because they might need to tell them they need to bail on them or they might want to try to salvage the situation on but I will take questions as we go I should have said that earlier Steve yeah um I guess I'm having difficulty with the other side I don't see why the conflict of interest defeats the privilege I mean I can see why the conflict of interest makes you think the advice is no good right yeah but I don't see what that's got to do with a privilege no I think that's a I think that's a fair question um and I I have to admit I want to think about that a little bit more as well the cases take it as a given that in other words that's the way they set it up they say we accept that this privilege operates but uh if the they say the law firm is in a it was a fiduciary relationship to its clients and if there is any conf any conflict of interest in that relationship the privileges as the courts say defeated the privilege just doesn't you cannot set up that privilege as against the beneficiary under this fiduciary relationship would be maybe another way that they they put it you have to disclose to the beneficiary under your fiduciary relationship I agree I'm not a hundred percent sure why that must be the case I you could be you could be in breach of your fiduciary obligations but still somehow be allowed to rely on a privilege but that's the way the American courts set the jurisprudence in motion they they say on the one hand we'll grant that the firms can have this privilege but they can't somehow maintain it if they're in a conflict of interest position it just seemed it just they take it that it would be wrong to allow the lawyer who owes these fiduciary obligations to rely on solicitor client privilege to the bed to the detriment of the beneficiary in a situation of conflict it's not like they analyze it as joint privilege right no not at all that they just say they and and bizarrely in the paper talks about the lens was the leading cases call this the fiduciary exception to solicitor client privilege which is strange because if the relationship is a fiduciary one any exception could be characterized as a fiduciary exception because it's a fiduciary relationship and what the paper says is it's not it's not really right to call it a fiduciary exception it's an exception founded on this conflict of interest right if you had an outside lawyer to that's right you can you'd be fine and and apart and again that's why that's in part what drive that's clearly what's driving the courts to say well of course the privilege must exist for in-house ethics council because why should it conceptually make any difference if i instead of going down the hallway to my own internal ethics council i pick up the phone and i actually retain outside council no question that would be privileged now there's no conflicting interest there because my that guy i've hired outside is in no way obliged to my original client so you don't have the conflict of interest problem the conflict of interest problem arises because you're using somebody who's internal to the firm and because the american cases are very aggressive in imputing the conflict from the original partner to the in-house ethics council so there is a difference between the in-house person and the external one yep at least factually it seems to me right because i think it's going to be very ambiguous when you walk down the hall whether you're walking down the hall to say in contemplation of litigation yes i want your advice yes or whether you're just saying what do you think i ought to do here i want to bounce some ideas off you because yeah yeah no and that's totally right and we will come to talk about that that's a kind of different issue which is the sort of agency versus principal issue in other words did you retain your internal person as principal meaning i want you to advise the firm versus did you retain this person as a flow through you're just acting as agent for your for the actual client and there'll be lots of certain there's no question about that i mean if i'm doing a transaction and i need some tax advice and i walk down the hall and i ask the tax partner hey how do we handle this and the tax partner says this how we handle no wait that's privileged that's not advising the firm that's advising on behalf of the client right that's because the the uh client is the ultimate client there in that in that circumstance so yeah one of the issues we're going to face is how do we just how could we meaningfully distinguish those two sorts of advice i think you can but we're certainly going to have to talk about that right how could we meaningfully distinguish those circumstances so the so the american law uh yeah i don't i can't see how that could attract privilege right because you don't have is a communication between a lawyer and a client right you can't be your own lawyer and client at the same time right then we get into the fool for a client part but that's a perhaps a separate aspect of that so the american law recognizes a privilege but then kind of ruins it right when it would be perhaps most important to to have it now this is some of these questions are great because they also they remind me to refer back to part of the earlier part of the paper there's an earlier chunk of the paper that actually walks through the rationale and benefits of in-house ethics council and the americans are clearly all over that right the aba actually says firms should have internal go-to ethics council they want that to be the operating practice for american firms and uh insurers right people who are writing you know the policies for law firms uh your premiums are in part dependent on whether you have in-house ethics council or not because the insurance companies think based on the statistical evidence and the information that they have that they're a better risk if they actually have somebody in-house who is handling ethics issues on behalf of the of the firm so there's a lot out there in the american context that wants this to operate and in a sense then we run into this problem where we kind of can't have it both ways if you want to do it this way as opposed to making you always have to go out in higher external counsel we've got it we've surely got to provide you with the con commitment benefits that you would get of doing it this way right we we can't sort of be trying to encourage you on the one hand to use an internal ethics council but take away one of the core hallmarks of that which would be a solicitor client privilege that you would get in respect to those communications that you would went if you that you would get if you went outside so the american jurisprudence more recently has been struggling with these concepts and we've had now a few cases that have come along and and i think changed the the landscape although i mean they're quite recent i mean i watched the video argument of one of the most recent ones which is a case out of the georgia court of appeals from 2012 and then just earlier this year it was argued in the georgia supreme court so depending on what the georgia supreme court does to the lower intermediate appellate court's decision the law is very much in flux on this but what the american courts is that they've said they've done a few things and this is also relevant to some broader themes in us ethics law which some of you will know has started to become less quick to just have these automatic imputations of of conflict that the the a b a has been under significant pressure and that a number of state bars have been moving much faster than the a b a in saying these automatic imputations of conflicts across large firms doesn't make the sense that conceptually maybe just we think should be happening on an automatic basis and so what the courts have been doing is that the sort of the jurisprudence has been moving in two directions one is to say we should be willing to look at this on a case by case basis rather than just automatically assume these conflicts are being imputed across to ethics council and that sets up some interesting ideas because what the what the cases and what the literature then gets into is well okay how would how would you just kind of back to Steve's question how would you what would you do on a case by case basis to kind of stop an imputation that for example the ethics council is in exactly the same position as the partner who's actually acting on the file and they talk about some things that are actually kind of familiar to us in a canadian landscape they talk about things like screening right they talk about things like ethical and information screening so for example if you had a ethics council who was a designated ethics council they were not somebody you would go to just to get some advice about an aspect of the transaction or what have you you would only be going to them because you needed advice quaw firm rather than for the client and so that so there's a number of layers you can build into that perhaps that person would not carry on any independent practice they would not actually have any clients they wouldn't handle client files their only client would be the firm they would be screened on an information basis from so they wouldn't be coming into contact generally with information about what was going on across the firm on various matters and cocktail parties lawyers would know this and they wouldn't say to their in-house ethic hey by the way and sort of just transfer information across there'd be this system of screening whereby you keep this person somewhat segregated the other form of screening that gets talked about is a financial screening right because one of the things we haven't talked about is well isn't the in-house ethics council going to have a financial like so let's say this client generates thousands of hours of billable revenue a year for the firm that puts the person in a conflict of interest in terms of whether you know do we say oh we got to dump this client or you know we got to send them elsewhere you know oh I don't want to do that if my if my bonus as ethics council hinges on those hours being generated then I have a financial conflict of interest problem so again you can you can if you choose to uh arguably set up screening for that sort of thing so you can say ethics council will be paid differently than other partners within the firm they may be paid on a flat pre-agreed amount they're not going to share in bonuses that might come off of particular transactions they're not going to have a cut of a draw based on you know aggregate hours build out to clients and and so forth so once you move beyond automatic imputation and automatically saying every lawyer in the firm has the same conflict as the original partner and you instead are willing to look at it on a case-by-case basis you at least conceptually can say we could create a case within our firm where our ethics council really was operating almost like they were an external council but they just happened to be located within our within our particular firm and the other thing that cases do there's a recent fiduciary and this is in a trust context it's not in a law firm context but there's a recent 2011 US Supreme Court decision on sort of fiduciary and trust laws about the extent to which fiduciaries can obtain their own legal advice right legal advice for them as fiduciary that doesn't somehow automatically flow through and have to be disclosed down to the beneficiary and that case was one of the sort of first in in this area to sort of cut through the chaff and kind of Steve's point again to say we have to ask that question were they being retained as council for the firm that is the fiduciary in that particular case or were they just as an agent for the ultimate beneficiary and that needs to be the vocal question and again that question can only be answered on a case-by-case basis you have to sort of look at the circumstances of each retention and say well were you doing that as agent or as principal and that's the that's kind of where the american story ends it's in flux but it's developing and the way I sign off on it is to say I think the US law is going to say there are two key hallmarks for this privilege which the cases say exists that the two hallmarks for this privilege being working that is not being defeated would be that your in house ethics council isn't in a conflict of interest in this narrower sense that is we're not going to just automatically impute it right but if we do a more focused analysis and they're not in a conflict of interest information finance that kind of stuff and they've been retained by the firm as principal if they meet those two criteria the privilege should survive the privilege should work and not be defeated right but if they've been retained in fact as a flow through for the client or they are in an actual conflict of interest the privilege will fail subject to this point of order the interrelation between those two aspects so then I say okay well that's the american law well how does that translate into the canadian content is the if we if we take what we now know about canadian ethics law does the analysis look the same is it is it different and in some ways it's it's similar and in some ways it's quite different so two the two points of similarity would be conflict of interest based on confidential information so the martin and gray problem so the paper walks through martin and gray and says well no if we were going to impute this information across everybody in the firm we'd have a problem because the ethics council would know everything the partner knows but we've already solved that problem under canadian ethics law martin and gray allows us to set up these ethical screens it allows us to hive off a particular lawyer within a firm in the context of lawyers migrating between firms why couldn't we do the same sort of thing for ethics council exactly as I discussed earlier so so we could manage the the conflict of information based on confidential information we could manage that through screening and we could do the same sort of things I talked about earlier with regards to pay in a canadian context to manage conflict potentially based on self-interest or financial interest and the agency argument works pretty much the same way in the canadian context we do have some good canadian cases about the ability of fiduciaries to obtain counsel for themselves that they don't have to pass through down and reveal to their the beneficiary under the fiduciary relationship the sticking point and the part that I've had the most trouble with and again I say trouble with maybe this isn't the greatest hallmark of legal scholarship but I kind of would like for the benefit for the reasons that I that I outline in the paper of why ethics council seems to be to be a good thing I kind of want this to work in Canada right so I'm not being very empirical about that I'm not sort of just sitting in judgment and saying oh no interesting idea but won't work in Canada I'd like to explore the case by which it could work in Canada because I think it would be beneficial for canadian for big canadian law firms to have ethics council because as some of us know they are starting to do this right big firms like McCarthy's and Blake's and Tory's do have people that they are designated as their ethics council to fill exactly this sort of role and that's something I think it's going to increase across canadian law firms but again the utility of that is going to be somewhat defeated if we can't among other things sort of privilege issues so well what's the sticking point well the sticking point is this Neil duty of loyalty problem because and that gets the paper into some sort of dangerous waters about the Federation's view versus the CBA's view on the duty of loyalty in that conflict of interest although even on even both of those are potentially problematic here's the problem if the bright line rule in Neil says that a law firm cannot act both for and against the current client then that just might be the end of it right there because the law firm is clearly still acting for the client during that period of time but the lawyer the in-house ethics council at the firm is clearly acting for the client for the firm against the client right at least in adverse interest to the client so on a very literal formulation of Neil we look like not because of money or confidential information but just this idea of loyalty we just look like we might not be able to make this work and even on the CBA's conception which would require a significant risk of impairment in the representation well I think you can make I think the client would certainly make the argument that now having my lawyer also acting for itself against me runs the risk of significantly impairing the quality of its representation of me so on either test on either test we have a problem for the duty of loyalty okay but if I want to make this work I then need an argument to try to overcome so and so I'm still playing with this I'm still this is where the most thinking I think still has to happen for me I step back for a second and I think all right look but the duty of loyalty is primarily first and foremost it's formulated in terms of client-client conflicts right in other words duties to one client versus duty to another it's not formulated it doesn't speak in terms of conflict in loyalty terms client on the one hand versus firm on the other hand and so maybe a conception of the duty of loyalty that would treat the relationship between the client and the firm somewhat differently than the relationship between two competing clients might help us and I and so I get interested in that and then I draw a bit of inspiration from some other context that seemed to me to be somewhat similar so if I'm the client and my firm presents me with a bill and I think it's ten thousand dollars too large but I carry on I don't I don't fire them or anything they're still my lawyers and they're still acting but I challenge the bill we wouldn't think that the law firm now was in a irreconcilable duty of loyalty somehow because of their loyalty to me as client they can't maintain no our bill is right and we'll fight you on that if we need to I mean we're that bill is correct and we're nobody would say the law firm has to somehow prefer the client's interest by slashing its bill because the client says it should the firm is clearly entitled to prefer its financial interest in getting paid that ten thousand dollars over the position that's being taken by the client if we take another context if the client uh let's say takes the you know really further step and actually sues the firm for malpractice we know that the firm is able to rely on confidential information obtained from the client to defend itself against the malpractice allegation and again we wouldn't expect the firm to have to just roll over and throw up its hands if the firm alleges any impropriety on the grounds that that's otherwise to do otherwise would be disloyal right you have to prefer the client's interest above the firm's interest like it seems to me a very strange conception of the duty of loyalty that you would have to always put the law firms in for second to the client's interest well if that's right maybe that's the out right that may maybe the argument here is it would it should not strike us and again the duty of loyalty is evolving we don't necessarily know all of its parameters yet it still has to be fleshed out maybe it should not strike us as a violation of a duty of loyalty that if a problem arose the lawyer and the firm would go to an internal in-house ethics council and receive advice for the firm as firm and that doing so is not violative of the duty of loyalty that that firm owes to its current client and I I have to I have to continue to think about this and I certainly I really welcome thoughts on that but I I have a sense that I think that I could live with that that I think I could support that being the the conclusion and that's that's kind of really where it is I didn't come in like to forget about this already but if the examples that you laterally gave I mean isn't it a fundamental principle of uh of fiduciary law that it can be waived uh so it's always that yep discretion of that's right of the agreement it's always subject to agreement of the party no that's right so if a client continues in the relationship with the lawyer either explicitly or implicitly in the understanding that the lawyer now has a conflict or the firm now has a conflict hasn't that client in fact waived their right to uh or or uh or should say amended the the the duty of loyalty that the firm owes to them to create that exception that that might be right um I guess one of my concerns I have there is that the the timing is the problem right so in other words the firm will go to its in-house ethics council to get this information before it raises even before out of any sense of candor at all it likely says anything to its client so so it isn't I agree it might be possible to say the partner let's say says to the client I'm worried about x I'm going to I now propose to go down the hall and talk to my in-house ethics council is that okay with you client and certainly if the client says that's okay you're fine I suppose another way you could do it is you could put it in the retainer most firms don't at the moment but you could you could you could have language in the retainer that says I explicitly agree that if an issue arises you will be allowed to go to your in-house ethics council and I won't seek to you know claim that somehow that's a communication I can I can get access to but if you if you haven't I just pick up yeah absolutely excuse me that's the most sensible and cleanest way to do this so the clients know upfront what relationship is and it goes to I guess the descent by McLaughlin in Strother who says that the fiduciary the nature of fiduciary relationship is dependent upon the definition in retainer essentially and that's a way out of the difficult Neil conundrum other right like so she's using it for the same sort of reason I would be using it right which is read too literally Neil is too big a problem I like that so why not just sort of make that the position instead of having to go the more indirect growth or sort of imputing stuff or implicitly or potentially weaving it no but I think you'd need both right because I don't think it would be right to say if it's not in the retainer it can't be done that that's what I because Wallace raises some of those issues too right I mean it's always easy after the fact to say why didn't you guys put this in the where didn't you address this in the retainer but we know it's not always going to be addressed in the retainer and I and I don't know that that should by definition mean this will fail well so I guess I see the obligation on law firms is not these issues have been raised right and the the antenna should be up and they want to have in-house counsel they want to do this then they should make sure they've set up an infrastructure to deal with this particular issue so I don't I think maybe if I make it purely contractual then you don't have real problems around right but but if I didn't but if I didn't let's let's go back to first principle so if I didn't make it pretty contractual why does the argument otherwise fall down like have I not found a way around the loyalty problem even in the absence of the contract I haven't then I have if I haven't I still have a problem but but if I've persuaded me to have okay it's not that you haven't no fair enough I need to sort of run probably a few things before I get to my real question okay is the assumption kind of on whatever side of anything we're on that you identify a problem and at some point you got to tell the client that you identify the problem you can't just say yeah I identified this problem I worked itself through and I think we're okay and therefore I'm never going to tell the client anything that's not on is that that actually there are circumstances where that maybe could be on that that could have like I mean you owe duty of candor to your client as well right so when when an issue arises that would get over whatever that threshold would be you would have to notify your client at least that there was this issue and that you've satisfied yourself on it okay but but but it I don't mean to be difficult but even the duty of candor would have a threshold somewhere right you don't have to tell your client everything you think of and but figure out you're okay okay but we've gone over that initial threat yep yep so and you you get down the file to your ethics counselor your ethics counselor says we screwed up or you screwed up really badly right and you know you've got to tell your client and it's gonna all have some breakers right the principal is supposed to follow through on that and let the chips follow what they made yeah what it seems to me in a case that's that bad the lawyer would have to go back down the hall to their client to the firm's client and say and as a result of the duty of candor say we we now you I don't think you have to give the game away I think your insurer would be pretty unhappy if you said we screwed up and you guys better go out and sue us you you'd say we are concerned that there may be a problem here and we can as a result no longer continue to act for you you will have to get new council and new council will have to figure out that you have a potential claim against us and we're gonna which we're gonna defend vigorously even if the ethics council thinks boy did you screw this up really badly this is the context where you don't want the ethics counselor's opinion saying you screwed up exactly exactly right exactly right I mean and and that's and that's the position and it's true in the american law as well I mean that the firms are saying every other internal entity gets to go to its in-house council and its in-house council writes this up and that's it's privileged right that doesn't see the light of day why if we do that in a law firm context should the client get in a sense this evidentiary windfall of getting to see ethics council saying boy did we screw this up and if we spin it forward the other way I mean if the ethics council thought that this wasn't privileged and could go out to the client why would they write it down yeah right I'm out I'm in the wake of some of the early american cases some academics tongue-in-cheekedly said that's what firms firms would stop writing it down they'd start just having telephone conversations about this stuff instead because they could they were worried that they just couldn't rely on the privilege and if the ethics counselor says ultimately looks fine yep explains why yep seems to me you'd probably want to give that to the client well if it's your privilege you could choose to yeah right but you might not want to like so that in other words ethics council say I'm worried about this this and this but on a judgment call I think we're okay so it still goes just too much of correct that would be the fear that would be a fear anyway seems to me that the insurer has to jump in by calling insurer as soon as you have uh you're on notice that there may be a problem you have to call them or you're going to put your insurance in jeopardy right so and then when you make that call they're going to give their advice to you probably to put you in somebody else's hands or tell you what to do or what not to do I think the insurance pieces are really big part of this yeah that when when the ethics counselor makes a determination that we've done something wrong or there's a good probability that we've done something wrong but uh that that may well be right um I don't know that that stops the generation of the communication in other words the papers the paper trail is still there for the client to try to access as again it's a timing quite like I'm not I'm just not sure what happened in practice it would happen faster and the other problem of course would be if the firm wants to try I mean firms do try to sort of save these situations rather than have them immediately go off to the worst case scenario and arguably we we should be wanting firms to try that's why they have an ethics comment the ethics council isn't just there to be the person who pulls the plug all the time that to some degree they have a role in trying to find the way through that manages this for both the client and the firm can I ask a question Stephen that really loops I think it loops back ultimately to some of your points about the American experience at both ends I don't I don't fully understand the reason why the existence of a conflict dissolves the privilege so I'm with Stephen in that being an outstanding question yeah but setting that assuming that that's the case for the moment then we're in the in the midst of exploring what would or would not constitute a conflict and that's the dilemma that you're identifying with respect to Canadian law right and I think in Sarah's and Richard's interventions they were suggesting about the way in which client consent can waive the conflict but I'm not entirely convinced of that for this reason which is that if you look at Neil and if you look at the model code or what the CBA has proposed consent can dissolve a conflict unless the lawyer's view is that his or her ability to fully represent the client is not itself compromised by the interest of another client or the lawyer's own interest right and it seems to me that that piece the lawyer's own interest is still on the table even though the client may have consented right and if the lawyer in this context is honest about it they might say we got the client's consent but jeez we we're not going to be able to champion the client's interest here because it's just like sticking a knife in our own backs and so it seems to me we're still left with that lawyer client conflict dilemma if that's the judgment you reached in can I just add one other feature to it that formulation also exists I think in the American restatement and in the ABA rules and so I'm curious to know whether that makes its appearance in the US cases that the lawyer client conflict because of the nature of the law firm's interest here seems to be on the table consistently as well it doesn't in the earlier sort of run of US cases because of the they get they don't get to that they the easy imputation just means they they find this they just find the conflict right out of the out of the gate and so they don't get to that more I think subtle question I think you raise a good question which would be let's say the more some of these more recent cases like this one under Georgia start becoming the way forward then maybe that question reappears does come out of the table now you you two would know this better than I mean is this is this in part played out by the the tension in strut there about sort of what you can how far you can go with consenting to things in the retainer because I agree with you there would be some things you couldn't waive right there there there gotta be some category of conflicts you can't wait or even if you waived the the structure is that the lawyer makes an honest judgment that he or she still has too much at stake themselves to be able to really champion the client's cause right which starts to feel like what's going on here right there's still a conflict right I think needed was that I'm not sure of McLaughlin would maybe not but she's so contractual in her view of things right so I think that's where they might actually might disagree in that I mean for for for Vinny there's to be the overarching point and that's for McLaughlin be but even in the even in the hard rule written by the Federation and the proposals by the CBA they're still prepared to talk about substantial risk that the lawyer identifies that base of conflict based on obligations to another client substantial risk to quality representation based on the representation of another client or the lawyer's own interests and it's it's hard to walk away from that even if you're Chief Justice McLaughlin because that's that might not put loyalty at the highest level but you don't want to dissolve it all together two issues though right I I could see how even with the consent even with the retainer the firm might think we've clearly got to send this client away and this client is going to be represented now by somebody else and we're now in an adversarial position we can't continue to act but that might not necessarily mean they also lose the privilege about the communication that they had with in-house counsel but that point might then depend on does the privilege go away because of a conflict which is the reason you sent the client away so it returns to that early somewhat confusing conclusion that these American courts seem to have started with and they get that they they seem to pull that from the nature of the fiduciary relationship that because it's a fiduciary relationship and you're attempting to set up a privilege vis-a-vis your beneficiary you can't do that if you're in a conflicted position and I have some some I mean I I can't I can't say to myself outright that that's got to be wrong even though I agree that there seems to be a bit of a conceptual mismatch between saying I mean you clearly can't say what difference does it make as to whether you're in a conflict of interest as to why you wouldn't have the privilege or I I understand that as a good conceptual question but I also can see where the courts are coming from and in saying that because otherwise in a sense there's no nothing is flowing from the from the breach right nothing's flowing from you having not lived up to your fiduciary obligations you're you're in breach of these fiduciary obligations vis-a-vis your client and yet you get to claim privilege over the communications so I think they're worried about that these have been very helpful questions so it's really really wonderful it's remarkable there's still the I'm trying to articulate I mean when you go back and you read sort of Benny's decision and you read and the Eddie Greenspan case the CBC and Stewart they put an awful lot of emphasis on the the justification for the initial fiduciary obligation is to maintain public confidence in the legal profession and I think you need we need to push out a bit harder as the it's not just it's a fiduciary relationship it's about how will people clients see I agree law firms if law firms seems if they're betraying their own client is that betrayal yeah moment so there's that grinding principle they've articulated as well and so maybe the issue is then can we separate the rules of what in-house council can do or sorry in-house ethics council can do they can do this this and this but they can't do this and you have to go to outside council for that that might be right although I suppose the question I'm looking at is much more limited one which is just whether privilege would attach to the communications as opposed to what their role could be right and the communications are usually going to proceed what they then might end up doing and further working on the matter I think that's fair there would be I'm sure there would be situations even with a firm that sets up proper screening and everything for its ethics council where the firm will choose to use outside council because the optics of doing that are better but we still have to figure out what happens to the communications that were generated about before that happened but before that that stage I mean we didn't talk about it in the presentation but so one of the concerns that I think is more prevalent in the US although I suppose I could see it arising here is cases where something comes up that actually is quite fundamental you are now you know you are in odds with your client and you know your client is very likely to sue you and yet you can't dump your client because you are in the middle of something where you need court consent to get off the record or you have a transaction that your corporate department is about to close or there will be very serious financial repercussions and so you get to a situation where on the one hand you have a set of ethical rules requiring you to continue to act and on another hand you have a set of ethical rules that require you to get off and it's that interim period where you bite the bullet and you say we are continuing to act because we have an obligation to do that but at the same time our in-house council is generating documents that we're going to use because we know this malpractice claim is coming and it just seems the argument the firm would make is we can't lose privilege over that because we were in good faith continue carrying we didn't you're pressing us for not pulling the plug more vigorously on the client in these cases and not screwing the morse right right but it's ironic in the sense that if you were to disclose it to the client they might fire you right on the spot right if you don't disclose it they're stuck because they don't know that you carry on and do the rest of the work competently right but if they only knew which by the privilege arrangement they can't they'd fire in a minute you can do exactly right yeah well i was like so how does the clock tick in all this i mean that's the same problem me at what point in this process do you realize that your interests have diverged and what part of the advice isn't covered as a consequence like presumably you have to have a conversation that predates that realization before you get there i guess i'm saying no i don't i don't know that i i it is quite possible i think that you would know the minute you walk in no no i think it's pop to the ethics council office yeah well you have a you have an inkling and you know i'm i'm i'm troubled with the idea of saying you'd always have to take that inkling first and foremost to the client somehow i mean you you might take that inkling first to your in-house ethics council because you're now there's a council might say no no it's fine just in fact you would think it a lot of you'd hope one of the reasons for having an ethics council is you'd go down the hall and your ethics council would say no you're good you're fine we're okay um and then the issue probably never even comes up with the client right it it's an alarm it's a little alarm that went off for you and you checked and you're fine but if the little alarm goes off and you check and your in-house ethics council says we got a we have a big problem here that's the most interesting scenario and then puts a finger on the tension between on the one hand the duty of candor right yeah and the fact that you're genuinely in a meaningful conflict of interest between your firm and the client and you're continuing to act and the client sitting in the office down the hall without knowing right no but you know so so the duty of candor is clearly going to require you to advise the client that something has happened that has created this conflict but by that point the communication has happened right you've you've gotten the you've obtained the advice from your ethics council we seem to be thinking in this situation there's no problem there's a big problem right you're okay right but you should really start doing these things that's right like if the advice is now start doing if it if it relates to the strategy or approaches to the case or the way in which you communicate with the client or what you that that in those in-between kind of spaces you might have to tell them more I'm going to do the of candor than you would if you had a big problem like so then you're like well we think there might be a problem you might have to tell them we think we now need to start doing the following things right I'm not sure you'd have to tell them or you'll have a claim again you know if we don't do these things it will be negligent for us and you will have a claim against us but to reveal the relationship that you stand in relation to others because otherwise the client could be instructing you what that actually does do to limit the capacity of the client to instruct you in certain ways around so it could limit the ways in which the lawyer can give counsel or can pursue the matter if they suddenly arrived in a situation where they're not they don't have a big problem and they don't have no problem but actually they have to navigate the terrain and the navigating of that current terrain will affect limit restrict or shape the particular strategy you take seems to me to be on a more of an epic like more of an obligation in terms of candor to say actually you can't instruct me this way in this way or we could do it this way but now as a counsel I'm limited in what I could do that another council might be able to do for you whereas if you have a big problem just sort of sort of say we don't know we might have a problem like you may have more of the duty to reveal but I I think that could be right I don't I don't the duty it seems to me the duty of candor is never going to require you just to be you know sentence turn over the opinion right you're they're going to tell you various things and based on the duty of candor you're going to have to have a sit down with your client and say certain things and you're I think going to be inclined to try to put a positive spin on it and say okay we have these issues but don't don't panic or jump out the window or something we have a we have a potential solution here and here's what we're going to attempt and get this to the extent that that opinion is shaping how you represent the client what you're able to do or willing to do on their behalf to keep your butt out of trouble is suddenly where you now have more of an obligation to reveal that there is this opinion from your in-house counsel that is shaping the choices that you're making on your client's behalf and that seems almost more problematic to me than what we really want to dwell which is a wow and that seems to me to get close to branch point about you start hitting a point where you just decide you can't do this you're gonna have to stop well no no but I do a positive spin thing yeah I can't I just can only do it these ways well if you're not in this parent with a client all right that you're doing it these ways because of what you're being told your butt out of the slum not because this is the best way to represent you yeah and do you get to bill for that too well that's I'm thinking about my no no no but this is clear the American cases say you've got to you've got to be kidding if you've docketed the hours that in-house counsel spent to the client's file to solve them for it there's there's no way you're gonna claim for you know the one of the indicia on a case-by-case test there's no way you could build there's no way you could have billed the client for the advice but imagine then the conversation where the client sees all these hours of work that aren't billed for because the firm does that and asks and the answer is that's all the work we did to get our asses out of a sling right right although they argue that they shouldn't see those hours at all right they wouldn't they wouldn't ever they wouldn't see a bill that says here's all these hours we're not building you just wouldn't disclose you the same way that again part of the project is to try to see to what extent under I guess American law first and then under Canadian law second we could mirror this like outside counsel because we know this all this is garden variety stuff for outside counsel for for uh McKinnis Cooper to pick up the phone and call Stuart McKelvie and say you know we have a problem we need to retain you it's we all of that's going to work right there isn't going to be a conflict and the communications will be privileged so if we want ethics counsel in-house to be a meaningful way for firms to move forward I think there is an agenda to actually try to find a conceptual way that it would work so why is it so important to salvage that so you mean to make it work like to make the in-house ethics counsel work like the question I'm asking is why is it so important to salvage that well the facts of these situations it plainly does not work well where does it work to justify well trying to make it work here so the paper talks about in some ways the benefits of it's a bit of an extrapolation from the general benefits of having in-house counsel right why would bell have in-house counsel well because they're more available and they know the business well and they know the people and they know the structure so there's all kinds of synergies you get from being able to use your own people rather than always having to go outside and yep that's another the ABA talks about that at length right they say having the person actually they are on the floor because we will see we're only talking about part of this right I mean at most firms that have an ethics counsel there's a both a proactive and a reactive role right and we we we obviously want the proactive role and that has all kinds of positive benefits it just so my I think the case to be made for why having big firms have in-house counsels is not a hard case to make but then the question is do you diminish in many ways the utility of that if you rob them of this privilege that that's the worry for me for that in the literature that's the concern and the case in which you're going to rob them of that privilege you can't tell in advance in a sense because you can't tell opinions right that's that's the pitch so you want to you want to be able to go to them right and like it like like normal solicitor client privilege it's really important to know the lay of the land before the communication happens right I mean you you need to have some degree of confidence that this is going to work right or you will be gun shy in some way right absolutely yeah that's the argument yeah well I think if you find Steven that it is robbed of its utility in its entirety you'll have opened up a wonderful career at post-academic career for Oath House Ethics Council Devlin and Al Ethics Council for hire I like the Oath House idea well I actually think we have a lot of retired judges do this right maybe yeah and not get paid for it right that would be better I guess yeah that would be something that would be something maybe on that thought we should try to close and thank Steven for a great seminar and thank everyone for participating it was a great question to get it very helpful for me thank you thank you thanks a lot yeah good job


So, in the previous lecture we have seen this good result that if you have a matrix A does not matter whether it is square or rectangular we can always get it to a row reduced echelon form right through a series of elementary row operations in which case we say that any matrix is row equivalent to a row reduced echelon form. So, now then it is only befitting that we show you what is the merit of this row reduced echelon form or why is this so desirable. So, the first thing I will do today is I will take up an example relatively simple example which I can hopefully walk out on the board but I also request you to work out with me because this involves a bit of calculations and I might go wrong on some of those steps. So, do correct me at any step when you find that my calculations are going wrong. So, let us take an example A x is equal to 0 and you might immediately say hang on you said you will be solving for A x is equal to b but now suddenly you are changing the rules of the game and saying I am going to solve for A x is equal to 0 why is this right. So, I just like you to hold on to that thought for a moment and just show you the analogy for instance when you solved differential equations. How did we go about it? We first found the complementary solution by considering that the right hand side of the differential equation is 0 and then we had this particular integral which told us what the particular solution for that particular differential equation when you have a certain kind of a forcing function would look like right. So, we are going to do this in this pretty much the same spirit and therefore this is like finding that complementary solution for the ODE. So, with that sort of intuition in place let us see what we can do with this. The point is that we have already seen that any matrix can be taken to a row reduced echelon form without altering the solution set. So, let us do that to this fellow too. The advantage is if you have a 0 on the right hand side it does not matter what sort of operations you do on this the same operation on the right hand side will still lead to a 0. The structure of the right hand side does not change through those row operations because it is already a 0.  So, let us say we get from here to the row reduced echelon form which is this. Let me just for the sake of completeness mention that this A is m cross n. So, we are going to try and see an example of this how you get to this just a bit of working out. Let me take this example let us say 2, 4, 6, 8, 1, 7, 4, 2 I hope I am not digging my own grave by choosing a rather complicated one. Let us see 4, 18, 14, 12. Suppose this is my A matrix and I want to get it to the row reduced echelon form. So, please check my calculations as I said earlier also. So, the first thing we do is we scan from the first row onwards. The first non-zero entry in the first row happens to be the first entry itself right. So, what do we do? We need to get a leading one here. So, I am not going to cook up those explicit matrices I am going to try and do a bit of mental calculation and show you what the next step would be. And in fact, I am going to try and combine multiple steps at one go which is why I might go wrong. So, from this let us just divide this by 2 throughout sorry yeah 2, 3, 4. But now the next goal is to generate 0's below the leading one that I have just obtained here for which what do I need to do? I need to just subtract this row from this right. So, the first one will just lead to 0 and 7 minus 2 is 5, 4 minus 3 is 1 and 2 minus 4 is minus 2. By the same token I need to subtract 4 times this row or 2 times this whichever way because we have already reduced it to the leading one. Let us consider this row because I am combining you see how many steps one operation of the first kind and 2 operations of the second kind in one step itself. So, that I am over and done with the first leading one and the entries below it in one go right. So, a lot of mental calculations may be but I hope you are following the bits. So, what is this? This minus 4 times this. So, already 0 here 18 minus 8 right. So, that is a 10 here 14 minus 12 that is 2 here no 14 minus 6 right 12 okay. So, that is a 2 I was right and 12 minus. So, this is 16 right. So, minus 4 yeah of course I cooked it up that way on the go. Now the next step is to look for the second leading one in the second row which happens to be this fellow right. So, I have to make this a 1 now. So, let us try and do that. So, notice that no matter what I do to this and scale it and add it to this, this leading one is unaffected because I have already generated 0s below it right. So, that is the reason why you must do one operation of the first kind followed by m minus 1 operations of the second kind because you have already gotten 0. So, any operation here after does not affect this leading one. So, what do you do? Divide this by 5 of course. So, let me write this second one first 1 1 5th and minus 2 5th right and then I have to subtract 2 times this row from the first. So, that I get a 0 here what happens 3 minus 2 5th right. So, what is it yeah 3 minus 2 5th is it not. So, 15 by 5 minus 2 by 5 that is 13 by 5 I hope again I am not erring and this is 4 minus plus because there is a minus sign already. So, 4 plus 4 by 5 right. So, 20 by 5 plus 4 by 5 that is 24 by 5 same thing I have to do here, but because I have cleverly chosen this I know what the answer is going to be in this case no chance of a calculation mistake and I urge you to check that you will already get 0's here just check right it is just twice this that is the way I had cooked it up right. So, is this in row reduced echelon form does it meet the condition it is row reduced of course and also this is k 1 is 1 k 2 is 2 the position of the first leading 1 is 1 the position of the second leading 1 is 2 and there are no other questions of any leading other other leading ones because there are only 2 non-zero rows. Now, by my claim here these 2 are equivalent systems. So, if I want to solve for A x is equal to 0 I might as well solve the same for R x is equal to 0. So, you might now say what is the benefit of this let us look at it. So, now I have to solve the following 1 0 13 by 5 24 by 5 0 1 1 5th minus 2 5th 0 0 0 and 0 and you have x 1 x 2 x 3 x 4 is equal to 0 what I am next going to do is the following you see these leading ones that I have generated it is not for nothing that I have focused my attention on them. The columns that contain the leading ones are going to be considered as what we call as the pivot ok. So, these 2 in this case are the pivots what does that translate to what do those 2 columns correspond to? The first column corresponds to x 1 and the second column corresponds to x 2. So, I immediately say that the columns that contain the leading ones are the pivot columns and so are the corresponding variables known as pivot variables. How many equations do you essentially have in this equivalent system now? The third one is just rendered meaningless it is 0 it is trivially true yeah. So, there are essentially 2 constraints just hold on to that thought again for a while. So, what does this first one say? I am going to write it in this manner where the pivot is the subject of the formula and the non pivot variables which we shall shortly assign as the free variables will be on the right hand side of this formula. So, what does that mean? This means it is minus 13 by 5 x 3 minus 24 by 5 x 4 and x 2 is going to be equal to minus 1 by 5 x 3 plus 2 by 5 x 4 right. So, where are we getting at with all this? Let me just erase these steps here ok the pivot variables and the non pivot variables. Let me name those non pivot variables by something else. Let us just say let x 3 is equal to u 1 x 4 is equal to u 2. Now, what does this whole vector x look like? Therefore, let us say that x 3 is equal to u 2 x 4 is equal to u 2. Now, what does this whole vector x look like? Therefore, x 1 x 2 x 3 x 4 is going to be equal to and this is how I am going to write this as u 1 plus u 2. So, can you tell me what this is going to be like? I have this as u 1 and this as u 2. So, what is x 1? See the pivot variables do not depend on each other. There is a decoupling already by virtue of the fact that I have gotten this all other entries below or above the pivot variables corresponding column to 0. Everything below the leading one and above the leading one is always a 0. So, they are decoupled. So, quite expectedly the expressions for the pivot variables will not involve each other. They will just depend on these so called non pivot variables or the free variables which are renamed it is just a relabeling really right. So, what is this x 1? It is minus 13 by 5 I presume minus 13 by 5 u 1 minus 24 by 5 u 2. About x 2 it is minus one-fifth and plus two-fifth minus one-fifth and two-fifth by the way these are just real numbers any arbitrary real number would suffice. What about x 3? By my very naming convention the definition I have given x 3 is what? Look at the non pivot variables. What do you notice so special about these non pivot variables? They have exactly one variable. They depend on exactly one variable and all the others will be 0. So, for example x 3 is representable just in terms of u 1 and it does not require any dependence on u 2. So, it is just this one here and a 0 here and this is 0 here and a 1 here. This structure is going to be very important. The fact that the pivot variables and these are the free variables look at this structure. What does this say? If I now try to generalize this for instance what can I say? Already you can observe something about this. Let us just point that out explicitly.  So, x need not be equal to 0. x is equal to 0 is of course one solution the trivial case when you put u 1 and u 2 both to be equal to 0, but even if u 1 and u 2 are not 0, but any arbitrary real number you will still be able to satisfy this. So, there are non-zero vectors that satisfy the equation A x is equal to 0, right. What is it that guarantees this? What sort of a situation guarantees this? That is what we are going to try and understand, but let us look at it in a more generic fashion now and try to understand what is going on. So, I will erase this particular example and I will write the expression. If you have any queries please feel free to stop me at any juncture. So, what I am going to write? Suppose you have A which is m cross n with m strictly less than n, yeah. This is what we call an under-determined system of equations, okay. When you are looking at A x is equal to 0 with m strictly less than n, it is an under-determined system of equation. In fact, A x is equal to b is also an under-determined system. Whenever m the number of rows is strictly less than the number of columns, it is under-determined.  Or you could call it a wide matrix if you do not want to body shame it, yeah.  What happens then? What can you say about the row reduced echelon form of a fat matrix, yeah. So, look at the row reduced, I am going to use the MATLAB notation, the row reduced echelon form of A. What can we say about this? Yes? Why? I am talking about the row reduced echelon form. What can you say about this immediately? Let us not get to linearly independent vectors now because we have not yet defined it, but we are just talking about the, we will talk about it in the language that we understand as yet. I understand where you are getting at, but let us just use the terms we have seen so far, you know, like terms like leading ones, echelon forms and so on. So, what can we say about this? How many rows are there? m. So, at most how many leading ones can you have? Because each row will have one leading one. So, total number of non-zero rows actually will have leading ones. So, at most m of those rows in the row reduced echelon form can be non-zero. So, the maximum number of leading ones is m. And what are we seeing the number of leading ones to correspond to? The pivot variables. Therefore, the maximum number of pivot variables is equal to n. What can we say about the number of free variables then? n minus m, which is strictly greater than 0. So, therefore, there exist free variables. And what can we say when we know that there exist free variables? These free variables can be freely assigned any arbitrary value, not just 0. Therefore, the moment I have free variables ready to be chosen at my beck and call, I can choose them to be non-zero. And therefore, I am always assured to have a non-zero solution to the equation A x is equal to 0. Make sense? Right? So, therefore, A x is equal to 0 must have a non-zero or sometimes we call it non-trivial solution. That is another way of seeing this in a slightly more sophisticated manner. If I want to write this down a little more formally not very, let us say you take the set 1, 2, 3 like this till n. What is this? The set of indices of all the variables, right? And there is this notation which is the subtraction of elements from a set to another. Let us take this to be k 1, k 2 till k r. What are these? These are exactly the positions of the pivot variables that is the leading ones in rows 1 through r which are the non-zero rows. This r can at most be m. So, therefore, this set let us not call it s, let us call it f. This set is non-empty. I mean I am just making the same argument as before only slightly more formally. Do you see the connection? It is the same argument, a little more technical presentation of the same argument. I am just saying these are the indices of all the variables. These are the indices of the pivot variables. If you take away the indices of the pivot variable from all the variables, from that of all the variables what you left with is the indices of the free variables. If the indices of the free variables is a non-empty set it means there exist free variables exactly this, right?  In fact, now that we have defined this set f already we are now in a position to describe the solution, the complete solution of this in a rather formal term. So, let us say this is it. So, I am going to write this x as a complete solution here and what is it going to look like? You will have certain pivot variables and certain free variables. So, suppose you have let us say this is our 10 tuple, okay. So, suppose a is say 3 cross 10. So, suppose a is say 3 cross 10 which means there are 10 variables and 3 equations and let us say you have 3 pivot variables so that there is no 0 of all 0s, right? What can you say? Suppose x1 the first position here x5 is the first position the fifth position and let us say the seventh position. So, x1 x5 and x3 are the pivot variables. What can we say about this? The first position it will be summation over ci times xi where i belongs to what set should it come from? You see the pivot variables we have seen in that example that we worked out the toy example they must be representable as combinations of the free variables alone. So, this must be for all the i that comes from this set f, agreed? Yeah, same thing can be made about or same sort of comment. So, let us say this is ci this is say bi whatever xi i belongs to free variables xi i belongs to free variables and this is say ai xi i belongs to free variables. What about the remaining entries? They will all correspond to some free variable or the other, right? So, you will have just maybe x2, x3, x4, x6, x8, x9, x10. Yeah, but we want to write this up in a better fashion still. So, can you guess what is coming up next? How am I going to write this down? Let us put all the free variables like so x3, x4, how many are there? Well, I should write something times x6 plus x6 plus x6 plus x6 ok then x8, 9, 10. So, x10, yeah x8 of course, I just missed x9 anyway you can just fill out and what can we say about the overall structure of these? See x2 will just have a 1 in the second entry. Will the second entry of any other vector have anything but a 0, right? It is just going to contain 0's everywhere except in this first vector. This is going to be incredibly important later when we talk about linear independence and other things of these vectors. Just bear that in mind we have not yet introduced the notion of linear independence. I am not going deep into that, but we will talk about it later. We will revisit this representation and what about the entries corresponding to x1, x5 and x7. So, how many vectors do you think are here? Exactly the as many as the number of free variables, right? So, do you now recall this picture that we had where I said that the total sum of the number of degrees of freedom and the number of constraints must be a fixed number and in fact that is equal to what? The total number of variables that is n, right? Is equal to the number of what? Leading once. That is nothing but the number of constraints, yeah? Because the number of leading ones is effectively the number of equations that you are looking to satisfy. The rest of them do not matter, is it not? Plus the number of free variables which is your degrees of freedom. In fact, at this juncture I might as well define the so called row rank of a matrix in the following manner. So, this is clear, right? I can erase this part. So, in fact we will say that the row rank of a matrix A can be defined as the number of numbers of non-zero rows or if you like you can call it the number of leading ones. It is all the same in R, R, E, F, A. Later we shall see that row rank and column rank does not matter is the same, not a very intuitive result. And therefore, in general we can get rid of the prefix row or column and we can just talk about rank of a matrix. Again, things for later, but now this is the way we can define the row rank. In that case, we can just say this N is equal to the rank plus the number of free variables, right? Getting close to the so called rank nullity theorem those of you who have encountered it earlier might immediately notice, right?