Basic matrix operations - Your turn

Matrices \(A\), \(B\), and \(C\) and vector \(\vec{b}\) are defined as:

\[\begin{split} A = \begin{bmatrix} 1 & 4 & 5 \\ 4 & 3 & 2 \\ -1 & 2 & 5 \end{bmatrix}, \qquad B = \begin{bmatrix} 2 & 3 & 6 \\ 2 & 2 & 1 \\ 4 & 5 & 7 \end{bmatrix}, \qquad C = \begin{bmatrix} 2 & 1 & 4 \\ 5 & 8 & 7 \\ 1 & 3 & 2 \\ 0 & 7 & 8 \end{bmatrix}, \qquad \vec{b} = \begin{bmatrix} 6 \\ 3 \\ 4 \end{bmatrix} \end{split}\]

Compute the following. If an operation is undefined, explain what Python does:
(a) \(BA\)
(b) \(CA\)
(c) \(AC\)
(d) \(AC^T\)

# TODO: Write your solution below

Next compute the following:
(e) Row reduce the augmented matrix \([A\ |\ \vec{b}]\).
(f) Row reduce the augmented matrix \([B\ |\ \vec{b}]\).

# TODO: Write your solution below