91Ó°ÊÓ

In Exercises \(5-8,\) the augmented matrix of a system of equations is given. Express the system in equation notation. $$\left(\begin{array}{rrrrr} 1 & 0 & 1 & 0 & 1 \\ 1 & -1 & 4 & -2 & 3 \\ 4 & 2 & 5 & 0 & 2 \end{array}\right)$$

Find AB. $$A=\left(\begin{array}{rrr} 1 & 5 & 9 \\ -2 & 3 & 3 \\ 1 & 7 & 0 \end{array}\right), \quad B=\left(\begin{array}{rrr} 2 & -3 & 0 \\ 4 & 5 & -1 \\ 0 & -1 & 1 \end{array}\right)$$

In Exercises \(5-8,\) the augmented matrix of a system of equations is given. Express the system in equation notation. $$\left(\begin{array}{rrrr} -1 & 0 & 2 & 6 \\ 0 & 5 & -4 & 1 \\ 8 & -2 & 3 & 4 \end{array}\right)$$

Use substitution to solve the system. $$\begin{aligned}&2 x-3 y=6\\\&5 x+7 y=2\end{aligned}$$

In Exercises \(9-12\), the reduced row echelon form of the augmented matrix of a system of equations is given. Find the solutions of the system. $$\left(\begin{array}{ccccc} 1 & 0 & 0 & 0 & 3 / 2 \\ 0 & 1 & 0 & 0 & 5 \\ 0 & 0 & 1 & 0 & -2 \\ 0 & 0 & 0 & 1 & 0 \end{array}\right)$$

Use substitution to solve the system. $$\begin{aligned}&3 x-2 y=4\\\&2 x+y=-1\end{aligned}$$

Find AB. $$A=\left(\begin{array}{rrr} 1 & 0 & -2 \\ 0 & 3 & -1 \\ 2 & 4 & 0 \end{array}\right), \quad B=\left(\begin{array}{ll} 1 & 1 \\ 1 & 0 \\ 0 & 1 \end{array}\right)$$

Find AB. $$A=\left(\begin{array}{rrr} -1 & 7 & 1 \\ -5 & 3 & 2 \\ 0 & 1 & 5 \\ -3 & 6 & 7 \end{array}\right), \quad B=\left(\begin{array}{rrrr} 7 & -2 & 6 & 2 \\ -2 & 8 & 4 & 1 \\ 0 & 7 & 0 & -5 \end{array}\right)$$

Use substitution to solve the system. $$\begin{aligned}&5 x-3 y=1\\\&5 x-2 y=-7\end{aligned}$$

In Exercises \(9-12\), the reduced row echelon form of the augmented matrix of a system of equations is given. Find the solutions of the system. $$\left(\begin{array}{ccccc} 1 & 0 & 0 & 0 & -1 \\ 0 & 1 & 0 & 0 & 3 \\ 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 \end{array}\right)$$