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Browse High School Linear Algebra
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Vector questions.

Rotation Matrix Using Trig Functions [12/15/2005]

Rotations in Three Dimensions [11/11/1999]

Row Operations and an Augmented Matrix [07/26/1999]
How can I solve a system of five simultaneous equations using row operations on the augmented matrix of the system?

Row-Reducing a Matrix [04/10/1998]
Could you please teach me how to row-reduce a matrix?

Shortest Distance between Points [01/17/1998]
I am doing a project on the shortest distance between two points via another plane. I need help with my theorems.

Shrunk Axes [01/20/1997]
How do you use the distance formula when the coordinate axes are not perpendicular?


Solving 3x3 Matrices Manually [01/27/1998]
How can I find the inverse of a 3x3 matrix manually (without pushing the inverse button on my calculator)?

Solving a 6x6 System of Equations [03/24/1998]
Is there a Cramer's rule for a 6x6 equation?


Solving Systems of Equations Using Matrices [04/02/1999]
Solve the following system of equations: a*(1-a) = b*c, b*(a+d-1) = 0, c*(a+d-1) = 0, d*(1-d) = b*c.

Solving Systems Using Augmented Matrices [11/05/1996]
How do you solve a set of linear equations using an augmented matrix?

Some Algebra Problems [6/1/1996]

The Stationary Vector [11/13/2000]
In Markov processes, what does a stationary vector tell you and how do you find it?


Subspace [01/25/2001]
Determine whether the following is a subspace of R^3...

Sum of Two Vectors [9/10/1996]
Why is the magnitude of the sum of two vectors less than or equal to the sum of the magnitudes of each vector?

Symmetric Matrices [10/27/1999]
Find all values of a, b, and c for which a 3x3 matrix A is symmetric, where the elements of A contain algebraic expressions in a, b, and c.

Symmetric Matrices in Everyday Life [05/20/2013]
A student wonders where in the real world a symmetric matrix might come up. Doctor George offers up two examples.


Three-Dimensional Cross Product Derivation [07/26/1999]
How can we prove the equation for 3-dimensional cross products in terms of the determinants a x (b x c) = (a.c)b - (a.b)c is correct?

Three-Dimensional Vectors [01/29/2003]

Two Dogs Pulling a Sled [10/15/2001]

Two Equations, Two Unknowns [7/27/1996]

Types of Linear Systems [10/13/1997]

Understanding Vector Spaces [03/14/2001]

Unit Vectors [07/02/2002]

Using an Augmented Matrix [11/21/1999]

Using Determinants to Find Area [06/09/1998]
How can you find the area of a triangle or a parallelogram using determinants?


Using Vectors to Prove Collinearity [06/05/1999]
How can I prove that the points of intersection of AB.DE, BC.EF, and CA.FD are collinear, if concurrent lines 0A, 0B, and 0C are produced to D, E, and F?

Values of Scalers [9/11/1996]
Can a scalar quantity be negative?

Variables Multiplied by Other Variables, Simplified Step by Step [08/22/2011]
If variables get multiplied by other variables in a system of equations, how do you solve it? or is it even possible? Doctor Vogler outlines several strategies, then -- reflecting on his choices at every turn -- methodically simplifies an example that requires lowering polynomial degree.


Vector Products and Possibilities [10/09/2012]
An engineer wonders how we come to define vector dot and cross products. Doctor Fenton derives the definition before Doctor Jacques reveals tensor, wedge, and other products.

Vector Proof [01/17/1999]

Vector Proof: Parallelogram Diagonals [01/20/1999]

Vectors and Orientation [05/29/2003]

Vectors of Parallelograms and Octagons [07/28/1998]

Vector Space Dimensions [12/09/1997]


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