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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 2/ Exercise solutions
Step1:  Definitions
E2.1
E2.2
Given the matrices $A=\begin{pmatrix}1 & 3 \ 4 & 5\end{pmatrix}$ and $B=\begin{pmatrix} -1 & 0 \ 3 & 3 \end{pmatrix}$, 
and the vectors $\vec{v}=\begin{pmatrix}1 \  2\end{pmatrix}$ and $\vec{w}=\begin{pmatrix}-3 \ -4\end{pmatrix}$,
compute the following expressions.
a) $A\vec{v}$
b) $B\vec{v}$
c) $A(B\vec{v})$
d) $B(A\vec{v})$
e) $A\vec{w}$
f) $B\vec{w}$
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Python Code:
# setup SymPy
from sympy import *
x, y, z, t = symbols('x y z t')
init_printing()
Explanation: 2/ Exercise solutions
End of explanation
# define the matrices A and B, and the vecs v and w
A = Matrix([[1,3],
            [4,5]])
B = Matrix([[-1,0],
            [ 3,3]])
v = Matrix([[1,2]]).T     # the .T makes v a column vector
w = Matrix([[-3,-4]]).T
# a)
A*v
# b)
B*v
# c)
A*B*v
# d)
B*A*v
# e)
A*w
# f)
B*w
Explanation: Definitions
E2.1
E2.2
Given the matrices $A=\begin{pmatrix}1 & 3 \ 4 & 5\end{pmatrix}$ and $B=\begin{pmatrix} -1 & 0 \ 3 & 3 \end{pmatrix}$, 
and the vectors $\vec{v}=\begin{pmatrix}1 \  2\end{pmatrix}$ and $\vec{w}=\begin{pmatrix}-3 \ -4\end{pmatrix}$,
compute the following expressions.
a) $A\vec{v}$
b) $B\vec{v}$
c) $A(B\vec{v})$
d) $B(A\vec{v})$
e) $A\vec{w}$
f) $B\vec{w}$
End of explanation
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