91Ó°ÊÓ

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

For the following exercises, solve the system of nonlinear equations using elimination. $$ \begin{array}{l} y^{2}-x^{2}=9 \\ 3 x^{2}+2 y^{2}=8 \end{array} $$

For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. $$ \frac{6 x}{x^{2}-4} $$

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

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

For the following exercises, write the linear system from the augmented matrix. $$ \left[\begin{array}{rrr|r} 4 & 5 & -2 & 12 \\ 0 & 1 & 58 & 2 \\ 8 & 7 & -3 & -5 \end{array}\right] $$

For the following exercises, solve the system of nonlinear equations using elimination. $$ \begin{array}{l} x^{2}+y^{2}+\frac{1}{16}=2500 \\ y=2 x^{2} \end{array} $$

For the following exercises, solve each system by elimination. $$ \begin{aligned} 5 x-2 y+3 z &=4 \\ -4 x+6 y-7 z &=-1 \\ 3 x+2 y-z &=4 \end{aligned} $$

For the following exercises, find the multiplicative inverse of each matrix, if it exists. $$ \left[\begin{array}{cc} -3 & 7 \\ 9 & 2 \end{array}\right] $$

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