91Ó°ÊÓ

Use any method to solve the system of nonlinear equations. $$ \begin{aligned} -2 x^{2}+y &=-5 \\ 6 x-y &=9 \end{aligned} $$

For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. $$\frac{2 x-3}{x^{2}-6 x+5}$$

For the following exercises, use the matrices below to perform scalar multiplication. $$ A=\left[\begin{array}{cc}{4} & {6} \\ {13} & {12}\end{array}\right], B=\left[\begin{array}{cc}{3} & {9} \\ {21} & {12} \\ {0} & {64}\end{array}\right], C=\left[\begin{array}{cccc}{16} & {3} & {7} & {18} \\\ {90} & {5} & {3} & {29}\end{array}\right], D=\left[\begin{array}{ccc}{18} & {12} & {13} \\ {8} & {14} & {6} \\ {7} & {4} & {21}\end{array}\right] $$ $$ \frac{1}{2} C $$

For the following exercises, find the multiplicative inverse of each matrix, if it exists. $$\left[\begin{array}{rr}-4 & -3 \\ -5 & 8\end{array}\right]$$

For the following exercises, solve each system by substitution. $$ \begin{aligned} 4 x+6 y+9 z &=0 \\\\-5 x+2 y-6 z &=3 \\ 7 x-4 y+3 z &=-3 \end{aligned} $$

Solve each system by substitution. $$ \begin{array}{r} x-0.2 y=1 \\ -10 x+2 y=5 \end{array} $$

For the following exercises, find the determinant. \(\left|\begin{array}{rrr}-1 & 4 & 0 \\ 0 & 2 & 3 \\ 0 & 0 & -3\end{array}\right|\)

Find the decomposition of the partial fraction for the nonrepeating linear factors. \(\frac{2 x-3}{x^{2}-6 x+5}\)

For the following exercises, use any method to solve the system of nonlinear equations. $$-2 x^{2}+y=-5$$ $$6 x-y=9$$

For the following exercises, solve the system by Gaussian elimination. $$ \left[\begin{array}{ll|l}{1} & {0} & {3} \\ {0} & {0} & {0}\end{array}\right] $$