91Ó°ÊÓ

In the following exercises, show that matrix \(A\) is the inverse of matrix \(B\). $$ A=\left[\begin{array}{cc} -2 & \frac{1}{2} \\ 3 & -1 \end{array}\right], \quad B=\left[\begin{array}{ll} -2 & -1 \\ -6 & -4 \end{array}\right] $$

For the following exercises, find the determinant. $$ \left|\begin{array}{rr} 1 & 0 \\ 3 & -4 \end{array}\right| $$

For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined. \(A=\left[\begin{array}{ll}1 & 3 \\ 0 & 7\end{array}\right], B=\left[\begin{array}{cc}2 & 14 \\ 22 & 6\end{array}\right], C=\left[\begin{array}{cc}1 & 5 \\ 8 & 92 \\ 12 & 6\end{array}\right], D=\left[\begin{array}{cc}10 & 14 \\ 7 & 2 \\ 5 & 61\end{array}\right], E=\left[\begin{array}{cc}6 & 12 \\ 14 & 5\end{array}\right], F=\left[\begin{array}{cc}0 & 9 \\ 78 & 17 \\ 15 & 4\end{array}\right]\) $$ B-E $$

For the following exercises, solve the system of nonlinear equations using substitution. $$ \begin{array}{r} y=-x \\ x^{2}+y^{2}=9 \end{array} $$

For the following exercises, write the augmented matrix for the linear system. $$ \begin{array}{l} x+5 y+8 z=19 \\ 12 x+3 y=4 \\ 3 x+4 y+9 z=-7 \end{array} $$

For the following exercises, determine whether the ordered triple given is the solution to the system of equations. $$ \begin{aligned} x-y &=0 \\ x-z &=5 \\ x-y+z=-1 \end{aligned} \quad \text { and }(4,4,-1) $$

For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. $$ \frac{10 x+47}{x^{2}+7 x+10} $$

For the following exercises, determine whether the ordered triple given is the solution to the system of equations. $$ \begin{aligned} -x-y+2 z &=3 \\ 5 x+8 y-3 z &=4 \quad \text { and }(4,1,-7) \\ -x+3 y-5 z &=-5 \end{aligned} $$

For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined. \(A=\left[\begin{array}{ll}1 & 3 \\ 0 & 7\end{array}\right], B=\left[\begin{array}{cc}2 & 14 \\ 22 & 6\end{array}\right], C=\left[\begin{array}{cc}1 & 5 \\ 8 & 92 \\ 12 & 6\end{array}\right], D=\left[\begin{array}{cc}10 & 14 \\ 7 & 2 \\ 5 & 61\end{array}\right], E=\left[\begin{array}{cc}6 & 12 \\ 14 & 5\end{array}\right], F=\left[\begin{array}{cc}0 & 9 \\ 78 & 17 \\ 15 & 4\end{array}\right]\) $$ C+F $$

For the following exercises, find the determinant. $$ \left|\begin{array}{rr} 10 & 20 \\ 0 & -10 \end{array}\right| $$