91Ó°ÊÓ

For the following exercises, find the multiplicative inverse of each matrix, if it exists. $$ \left[\begin{array}{cc} 0.5 & 1.5 \\ 1 & -0.5 \end{array}\right] $$

For the following exercises, find the determinant. $$ \left|\begin{array}{rrr} -2 & 1 & 4 \\ -4 & 2 & -8 \\ 2 & -8 & -3 \end{array}\right| $$

For the following exercises, solve the system by Gaussian elimination. $$ \left[\begin{array}{rr|r} -1 & 2 & -3 \\ 4 & -5 & 6 \end{array}\right] $$

For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. $$ \frac{3 x-1}{x^{2}-5 x+6} $$

For the following exercises, use any method to solve the system of nonlinear equations. $$ \begin{aligned} x^{2}+y^{2} &=1 \\ y &=-x^{2} \end{aligned} $$

For the following exercises, solve each system by Gaussian elimination. $$ \begin{array}{c} 2 x+3 y-6 z=1 \\ -4 x-6 y+12 z=-2 \\ x+2 y+5 z=10 \end{array} $$

For the following exercises, find the multiplicative inverse of each matrix, if it exists. $$ \left[\begin{array}{ccc} 1 & 0 & 6 \\ -2 & 1 & 7 \\ 3 & 0 & 2 \end{array}\right] $$

For the following exercises, find the determinant. $$ \left|\begin{array}{rrr} 6 & -1 & 2 \\ -4 & -3 & 5 \\ 1 & 9 & -1 \end{array}\right| $$

For the following exercises, solve each system by Gaussian elimination. $$ \begin{array}{c} 4 x+6 y-2 z=8 \\ 6 x+9 y-3 z=12 \\ -2 x-3 y+z=-4 \end{array} $$

For the following exercises, use any method to solve the system of nonlinear equations. $$ \begin{array}{r} 2 x^{3}-x^{2}=y \\ y=\frac{1}{2}-x \end{array} $$