91Ó°ÊÓ

For Problems \(13-26\), compute \(A B\) and \(B A\). $$ A=\left[\begin{array}{rr} -3 & -5 \\ 2 & 4 \end{array}\right], \quad B=\left[\begin{array}{rr} -2 & -\frac{5}{2} \\ 1 & \frac{3}{2} \end{array}\right] $$

For Problems \(19-26\), compute \(A B\). $$ A=\left[\begin{array}{rr} -3 & -5 \\ 4 & -7 \end{array}\right], \quad B=\left[\begin{array}{r} -3 \\ -10 \end{array}\right] $$

For Problems 21-36, use the technique discussed in this section to find the multiplicative inverse (if one exists) of each matrix. $$ \left[\begin{array}{rr} -3 & 1 \\ 3 & -2 \end{array}\right] $$

For Problems \(27-30\), use the following matrices. \(\begin{aligned} &A=\left[\begin{array}{rr} -2 & 3 \\ 5 & 4 \end{array}\right] \quad B=\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right]\\\ &C=\left[\begin{array}{ll} 1 & 0 \\ 1 & 0 \end{array}\right] \quad D=\left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right]\\\ &I=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right] \end{aligned}\) $$ \text { Compute } A B \text { and } B A \text {. } $$

For Problems 21-36, use the technique discussed in this section to find the multiplicative inverse (if one exists) of each matrix. $$ \left[\begin{array}{lll} 1 & 2 & 3 \\ 1 & 3 & 4 \\ 1 & 4 & 3 \end{array}\right] $$

For Problems \(27-30\), use the following matrices. \(\begin{aligned} &A=\left[\begin{array}{rr} -2 & 3 \\ 5 & 4 \end{array}\right] \quad B=\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right]\\\ &C=\left[\begin{array}{ll} 1 & 0 \\ 1 & 0 \end{array}\right] \quad D=\left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right]\\\ &I=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right] \end{aligned}\) $$ \text { Compute } A C \text { and } C A \text {. } $$

For Problems 27-40, use the method of matrix inverses to solve each system. $$ \left(\begin{array}{c} 2 x+3 y=13 \\ x+2 y=8 \end{array}\right) $$

For Problems 27-40, use the method of matrix inverses to solve each system. $$ \left(\begin{array}{rl} 4 x-3 y & =-23 \\ -3 x+2 y & =16 \end{array}\right) $$

For Problems 21-36, use the technique discussed in this section to find the multiplicative inverse (if one exists) of each matrix. $$ \left[\begin{array}{rrr} 1 & -2 & 1 \\ -2 & 5 & 3 \\ 3 & -5 & 7 \end{array}\right] $$

For Problems \(27-30\), use the following matrices. \(\begin{aligned} &A=\left[\begin{array}{rr} -2 & 3 \\ 5 & 4 \end{array}\right] \quad B=\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right]\\\ &C=\left[\begin{array}{ll} 1 & 0 \\ 1 & 0 \end{array}\right] \quad D=\left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right]\\\ &I=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right] \end{aligned}\) $$ \text { Compute } A D \text { and } D A \text {. } $$