Chapter 7

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

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

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

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

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

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

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

For the following exercises, solve the system by Gaussian elimination. $$ \left[\begin{array}{ll|l} 1 & 0 & 1 \\ 1 & 0 & 2 \end{array}\right] $$

For the following exercises, use the matrices below to perform scalar multiplication. \(A=\left[\begin{array}{rr}4 & 6 \\ 13 & 12\end{array}\right], B=\left[\begin{array}{rr}3 & 9 \\ 21 & 12 \\ 0 & 64\end{array}\right], C=\left[\begin{array}{cccc}16 & 3 & 7 & 18 \\ 90 & 5 & 3 & 29\end{array}\right], D=\left[\begin{array}{rrr}18 & 12 & 13 \\ 8 & 14 & 6 \\\ 7 & 4 & 21\end{array}\right]\) $$ 100 D $$

For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. $$ \frac{4 x-1}{x^{2}-x-6} $$

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

For the following exercises, solve each system by Gaussian elimination. $$ \begin{array}{c} 2 x-y+3 z=17 \\ -5 x+4 y-2 z=-46 \\ 2 y+5 z=-7 \end{array} $$

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

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

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

For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. $$ \frac{4 x+3}{x^{2}+8 x+15} $$

For the following exercises, use any method to solve the system of nonlinear equations. $$ \begin{aligned} x^{2}+y^{2} &=1 \\ y &=20 x^{2}-1 \end{aligned} $$

For the following exercises, solve each system by Gaussian elimination. $$ \begin{array}{c} 5 x-6 y+3 z=50 \\ -x+4 y=10 \\ 2 x-z=10 \end{array} $$

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

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

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 determinant. $$ \left|\begin{array}{rrr} 6 & -1 & 2 \\ -4 & -3 & 5 \\ 1 & 9 & -1 \end{array}\right| $$

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, solve the system by Gaussian elimination. $$ \left[\begin{array}{rr|r} -2 & 0 & 1 \\ 0 & 2 & -1 \end{array}\right] $$

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

For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. $$ \frac{-5 x-19}{(x+4)^{2}} $$

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

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

For the following exercises, find the multiplicative inverse of each matrix, if it exists. $$ \left[\begin{array}{ccc} 0 & 1 & -3 \\ 4 & 1 & 0 \\ 1 & 0 & 5 \end{array}\right] $$

For the following exercises, solve the system by Gaussian elimination. $$ \begin{array}{c} 2 x-3 y=-9 \\ 5 x+4 y=58 \end{array} $$

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

For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. $$ \frac{x}{(x-2)^{2}} $$

For the following exercises, use any method to solve the system of nonlinear equations. $$ \begin{array}{l} 9 x^{2}+25 y^{2}=225 \\ (x-6)^{2}+y^{2}=1 \end{array} $$

For the following exercises, solve each system by Gaussian elimination. $$ \begin{aligned} 2 x+3 y-4 z &=5 \\ -3 x+2 y+z &=11 \\ -x+5 y+3 z &=4 \end{aligned} $$

For the following exercises, find the determinant. $$ \left|\begin{array}{rrr} 1.1 & 2 & -1 \\ -4 & 0 & 0 \\ 4.1 & -0.4 & 2.5 \end{array}\right| $$

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

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

For the following exercises, use any method to solve the system of nonlinear equations. $$ \begin{array}{l} x^{4}-x^{2}=y \\ x^{2}+y=0 \end{array} $$

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, find the determinant. $$ \left|\begin{array}{rrr} 2 & -1.6 & 3.1 \\ 1.1 & 3 & -8 \\ -9.3 & 0 & 2 \end{array}\right| $$

For the following exercises, find the multiplicative inverse of each matrix, if it exists. $$ \left[\begin{array}{ccc} 1 & 9 & -3 \\ 2 & 5 & 6 \\ 4 & -2 & 7 \end{array}\right] $$

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