Quote:

$\displaystyle \text{1) Find the matrix product, if possible.}$

. . $\displaystyle \begin{pmatrix} 6 & 0 &\text{-}4 \\ 1 & 2 & 5 \\ 10 & \text{-}1 & 3 \end{pmatrix} \begin{pmatrix}1 \\ 2 \\ 3 \end{pmatrix}$

$\displaystyle \text{Answer: }\;\begin{pmatrix}\text{-}6 \\ 15 \\ 17 \end{pmatrix}$ Quote:

$\displaystyle \text{ 2) Decide whether the given matrices are inverses of each other.}$

. . .$\displaystyle \text{(Check to see if their product is the identity matrix }I.)$

. . $\displaystyle \begin{pmatrix}1 & 0 & 0 \\ \text{-}1 & \text{-}2 & 3 \\ 0 & 1 & 0 \end{pmatrix} \begin{pmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ \frac{1}{3} & \frac{1}{3} & \frac{2}{3} \end{pmatrix}$