Find each matrix product, if possible.\

$$\left[\begin{array}{ll}5 & 2 \\ 7 & 6 \\ 1 & 0\end{array}\right]\left[\begin{array}{rrr}1 & 4 & 0 \\ 2 & -1 & 2\end{array}\right]$$

Use the Gauss-Jordan method to solve each system of equations.

$$\begin{array}{r} x+2 y=5 \\ 2 x+y=-2 \end{array}$$

Find the inverse, if it exists, for each matrix.\

$$\left[\begin{array}{rrr}1 & 3 & 0 \\ 0 & 2 & -1 \\ 1 & 0 & 2\end{array}\right]$$

Suppose someone says that a more reasonable way to multiply two matrices than the method presented in the text is to multiply corresponding elements. For example, the result of

$$\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right] \cdot\left[\begin{array}{rr}3 & 5 \\ 7 & 11\end{array}\right]$$

should be

$$\left[\begin{array}{rr}3 & 10 \\ 21 & 44\end{array}\right]$$

, according to this person. How would you respond?

Find the values of the variables in each equation.\

$$\left[\begin{array}{ll}9 & 7 \\ r & 0\end{array}\right]=\left[\begin{array}{cc}m-3 & n+5 \\ 8 & 0\end{array}\right]$$