Additional matrix operations - Your turn

Consider the following matrices and vectors:

\[\begin{split} A = \begin{bmatrix} 3 & 2 & 3 \\ 3 & 1 & 5 \\ -4 & 6 & 1 \end{bmatrix}, \qquad B = \begin{bmatrix} 4 & 1 & -5 \\ 4 & 1 & 0 \\ -2 & 3 & 8 \end{bmatrix}, \qquad \vec{b} = \begin{bmatrix} 2 \\ 4 \\ 9 \end{bmatrix} \end{split}\]

Compute the following.
(a) \(A^{-1}\)
(b) \(B^{-1}\)
(c) \(\mathrm{det}(A)\)
(d) \(\mathrm{det}(B)\)
(e) Solve the system \(A \vec{x} = \vec{b}\) for \(\vec{x}\).
(f) Solve the system \(B \vec{x} = \vec{b}\) for \(\vec{x}\).

# TODO: Write your solution below

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