91Ó°ÊÓ

Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why. $$\left[\begin{array}{c}C+D \\ D-2 E \\ 3 E\end{array}\right]=\left[\begin{array}{l}3 \\ 2 \\ 6\end{array}\right]$$

Perform the indicated multiplications. $$\left[\begin{array}{rr} -8 & \frac{3}{2} \\ \frac{1}{3} & -6 \\ 2 & 8 \end{array}\right]\left[\begin{array}{rr} 2 & -3 \\ 4 & 5 \end{array}\right]$$

Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why. $$\left[\begin{array}{c}2 x-3 y \\ x+4 y\end{array}\right]=\left[\begin{array}{c}13 \\ 1\end{array}\right]$$

Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. $$\begin{aligned} &3 s+4 t-u=-5\\\ &2 u-6 s-8 t=10 \end{aligned}$$

Perform the indicated multiplications. $$\left[\begin{array}{cc} 12 & -47 \\ 43 & -18 \\ 36 & -22 \end{array}\right]\left[\begin{array}{rr} 1 & 2 \\ -1 & 1 \end{array}\right]$$

Solve the given systems of equations by using the inverse of the coefficient matrix. The numbers in parentheses refer to exercises from Section \(16.3,\) where the inverses may be checked. $$\begin{aligned} &x+3 y+2 z=5\\\ &-2 x-5 y-z=-1\\\ &2 x+4 y=-2 \end{aligned}$$

Use the given value of the determinant at the right and the properties of this section to evaluate the following determinants. $$\left|\begin{array}{rrr} 2 & -3 & 1 \\ -4 & 1 & 3 \\ 1 & -3 & -2 \end{array}\right|=40$$ $$\left|\begin{array}{rrr} 2 & -3 & 3 \\ -4 & 1 & 9 \\ 1 & -3 & -6 \end{array}\right|$$

Perform the indicated multiplications. $$\left[\begin{array}{rr} -1 & 7 \\ 3 & 5 \\ 10 & -1 \\ -5 & 12 \end{array}\right]\left[\begin{array}{rr} 2 & 1 \\ 5 & -3 \end{array}\right]$$

Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why. $$\left[\begin{array}{cc}x-3 & x+y \\ x-z & y+z \\ x+t & y-t\end{array}\right]=\left[\begin{array}{cr}5 & 3 \\ 4 & -1\end{array}\right]$$

Solve the given systems of equations by using the inverse of the coefficient matrix $$\begin{aligned} &2 x-3 y=3\\\ &4 x-5 y=4 \end{aligned}$$