91Ó°ÊÓ

For the following exercises, find the multiplicative inverse of each matrix, if it exists. $$\left[\begin{array}{rrr}1 & 2 & -1 \\ -3 & 4 & 1 \\ -2 & -4 & -5\end{array}\right]$$

Solve each system by Gaussian elimination. $$ \begin{aligned} 10 x+2 y-14 z &=8 \\ -x-2 y-4 z &=-1 \\ -12 x-6 y+6 z &=-12 \end{aligned} $$

Find the decomposition of the partial fraction for the repeating linear factors. \(\frac{7 x+14}{(x+3)^{2}}\)

For the following exercises, solve the system by Gaussian elimination. $$ \begin{array}{l}{6 x+2 y=-4} \\ {3 x+4 y=-17}\end{array} $$

For the following exercises, solve each system by Gaussian elimination. $$ \begin{aligned} 10 x+2 y-14 z &=8 \\\\-x-2 y-4 z &=-1 \\\\-12 x-6 y+6 z &=-12 \end{aligned} $$

For the following exercises, use the matrices below to perform matrix multiplication. $$ A=\left[\begin{array}{rr}{-1} & {5} \\ {3} & {2}\end{array}\right], B=\left[\begin{array}{rrr}{3} & {6} & {4} \\ {-8} & {0} & {12}\end{array}\right], C=\left[\begin{array}{rr}{4} & {10} \\ {-2} & {6} \\\ {5} & {9}\end{array}\right], D=\left[\begin{array}{rrr}{2} & {-3} & {12} \\\ {9} & {3} & {1} \\ {0} & {8} & {-10}\end{array}\right] $$ $$ D C $$

For the following exercises, use the matrices below to perform matrix multiplication. $$ A=\left[\begin{array}{rr}{-1} & {5} \\ {3} & {2}\end{array}\right], B=\left[\begin{array}{rrr}{3} & {6} & {4} \\ {-8} & {0} & {12}\end{array}\right], C=\left[\begin{array}{rr}{4} & {10} \\ {-2} & {6} \\\ {5} & {9}\end{array}\right], D=\left[\begin{array}{rrr}{2} & {-3} & {12} \\\ {9} & {3} & {1} \\ {0} & {8} & {-10}\end{array}\right] $$ $$ C B $$

For the following exercises, solve the system by Gaussian elimination. $$ \begin{aligned} 2 x+3 y &=12 \\ 4 x+y &=14 \end{aligned} $$

Use any method to solve the system of nonlinear equations. $$ \begin{array}{r} 2 x^{3}-x^{2}=y \\ x^{2}+y=0 \end{array} $$

Solve the system by Gaussian elimination. \(2 x+3 y=12\) \(4 x+y=14\)