91Ó°ÊÓ

Use Cramer's Rule to solve each system. $$\left\\{\begin{array}{c}x-2 y=5 \\\5 x-y=-2\end{array}\right.$$

In Exercises \(13-18,\) use the fact that if \(A=\left[\begin{array}{ll}a & b \\\ c & d\end{array}\right]\), then \(A^{-1}=\frac{1}{a d-b c}\left[\begin{array}{cc}d & -b \\ -c & a\end{array}\right]\) to find the inverse of cach matrix, if possible. Check that \(A A^{-1}=I_{2}\) and \(A^{-1} A=I_{2}\) $$A=\left[\begin{array}{rr}0 & 3 \\\4 & -2\end{array}\right]$$

Find the following matrices: a. \(A+B\) b. \(A-B\) c. \(-4 A\) d. \(3 A+2 B\) $$A=\left[\begin{array}{rrr}2 & -10 & -2 \\\14 & 12 & 10 \\\4 & -2 & 2 \end{array}\right], \quad B=\left[\begin{array}{rrr}6 & 10 & -2 \\\0 & -12 & -4 \\ -5 & 2 & -2\end{array}\right]$$

Use Cramer's Rule to solve each system. $$\left\\{\begin{array}{l}4 x-5 y=17 \\\2 x+3 y=3\end{array}\right.$$

Use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. $$\left\\{\begin{array}{l}2 x+y-z=2 \\\3 x+3 y-2 z=3\end{array}\right.$$

perform each matrix row operation and write the new matrix. $$ \left[\begin{array}{rrr|r} 1 & -3 & 2 & 0 \\ 3 & 1 & -1 & 7 \\ 2 & -2 & 1 & 3 \end{array}\right] $$ $$ -3 R_{1}+R_{2} $$

Use Cramer's Rule to solve each system. $$\left\\{\begin{array}{l}3 x+2 y=2 \\\2 x+2 y=3\end{array}\right.$$

Use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. $$\left\\{\begin{array}{r}3 x+2 y-z=5 \\\x+2 y-z=1\end{array}\right.$$

perform each matrix row operation and write the new matrix. $$ \left[\begin{array}{rrr|r} 1 & -1 & 5 & -6 \\ 3 & 3 & -1 & 10 \\ 1 & 3 & 2 & 5 \end{array}\right]-3 R_{1}+R_{2} $$

Find the following matrices: a. \(A+B\) b. \(A-B\) c. \(-4 A\) d. \(3 A+2 B\) $$A=\left[\begin{array}{rrr}6 & -3 & 5 \\\6 & 0 & -2 \\\\-4 & 2 & -1\end{array}\right], \quad B=\left[\begin{array}{rrr}-3 & 5 & 1 \\\\-1 & 2 & -6 \\\2 & 0 & 4\end{array}\right]$$