91Ó°ÊÓ

Find the inverse of each of the given matrices by using a calculator. $$\left[\begin{array}{rrr} 1 & 3 & 4 \\ -1 & -4 & -2 \\ 4 & 9 & 20 \end{array}\right]$$

Find the inverse of each of the given matrices by using a calculator. $$\left[\begin{array}{rrr} 2 & 4 & 0 \\ 3 & 4 & -2 \\ -1 & 1 & 2 \end{array}\right]$$

Solve the given system of equations by using the rref feature on a calculator. $$\begin{aligned} &7 x+5 y-3 z=16\\\ &3 x-5 y+2 z=-8\\\ &5 x+3 y-7 z=0 \end{aligned}$$

Determine whether or not \(B=A^{-1}\) $$A=\left[\begin{array}{rrr} 1 & -2 & 3 \\ 2 & -5 & 7 \\ -1 & 3 & -5 \end{array}\right] \quad B=\left[\begin{array}{rrr} 4 & -1 & 1 \\ 3 & -2 & -1 \\ 1 & -1 & -1 \end{array}\right]$$

Use matrices \(A, B, C,\) and \(D\) to find the indicated matrices. If the operations cannot be performed, explain why. $$\begin{aligned} &A=\left[\begin{array}{ll} 6 & -3 \\ 4 & -5 \end{array}\right] \quad B=\left[\begin{array}{rr} 3 & 12 \\ -9 & -6 \end{array}\right]\\\ &C=\left[\begin{array}{rrr} -1 & 4 & -7 \\ 2 & -6 & 11 \end{array}\right] \quad D=\left[\begin{array}{rrr} 7 & 9 & -6 \\ -4 & 0 & 8 \end{array}\right] \end{aligned}$$ $$B-3 A$$

Solve the given systems of equations by determinants. Evaluate by using a calculator. $$\begin{aligned} &2 x+y+z=2\\\ &3 y-z+2 t=4\\\ &y+2 z+t=0\\\ &3 x+2 z=4 \end{aligned}$$

Solve the given systems of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the results and the check. See Example 4. $$\begin{aligned} &x-5 y+2 z-t=-18\\\ &3 x+y-3 z+2 t=17\\\ &4 x-2 y+z-t=-1\\\ &-2 x+3 y-z+4 t=11 \end{aligned}$$

Solve the given systems of equations by determinants. Evaluate by using a calculator. $$\begin{aligned} &6 x+3 y+3 z=0\\\ &x-y+2 t=2\\\ &2 y+z+4 t=2\\\ &5 x+2 z+2 t=4 \end{aligned}$$

Find the inverse of each of the given matrices by using a calculator. $$\left[\begin{array}{rrr} 10 & -5 & 30 \\ -2 & 4 & -5 \\ 20 & 5 & 5 \end{array}\right]$$

Solve the given system of equations by using the rref feature on a calculator. $$\begin{aligned} &x+y+z=6\\\ &2 y+5 z=-4\\\ &2 x+5 y-z=27 \end{aligned}$$