91Ó°ÊÓ

In the following exercises, solve each system of equations using a matrix. $$ \left\\{\begin{array}{l} x+2 y+z=4 \\ x+y-2 z=3 \\ -2 x-3 y+z=-7 \end{array}\right. $$

Solve the system of equations \(\left\\{\begin{array}{l}x+y=10 \\\ x-y=6\end{array}\right.\) a) by graphing and (b) by substitution. (c) Which method you prefer? Why?

Solve the system of equations \(\left\\{\begin{array}{l}3 x+y=12 \\\ x=y-8\end{array}\right.\) by substitution and explain all your steps in words.

In the following exercises, evaluate the determinate of each square matrix. $$ \left[\begin{array}{ll} 6 & -2 \\ 3 & -1 \end{array}\right] $$

In the following exercises, evaluate the determinate of each square matrix. $$ \left[\begin{array}{ll} -4 & 8 \\ -3 & 5 \end{array}\right] $$

In the following exercises, evaluate the determinate of each square matrix. $$ \left[\begin{array}{rr} -3 & 5 \\ 0 & -4 \end{array}\right] $$

In the following exercises, evaluate the determinate of each square matrix. $$ \left[\begin{array}{rr} -2 & 0 \\ 7 & -5 \end{array}\right] $$

In the following exercises, evaluate each determinant by expanding by minors along the first row.$$ \left|\begin{array}{rrr} -2 & 3 & -1 \\ -1 & 2 & -2 \\ 3 & 1 & -3 \end{array}\right| $$

In the following exercises, evaluate each determinant by expanding by minors along the first row. $$ \left|\begin{array}{rrr} -2 & -3 & -4 \\ 5 & -6 & 7 \\ -1 & 2 & 0 \end{array}\right| $$

In the following exercises, evaluate each determinant by expanding by minors along the first row. $$ \left|\begin{array}{rrr} 1 & 3 & -2 \\ 5 & -6 & 4 \\ 0 & -2 & -1 \end{array}\right| $$