Question $12$ $\newline$ $0 / 10$ pts $\newline$ $5$ $\newline$ $98$ $\newline$ Details $\newline$ Let $A=\left[\begin{array}{cc}-3 & -4 \\ 0 & 4 \\ -4 & -2\end{array}\right], B=\left[\begin{array}{cc}-4 & 0 \\ -3 & 0 \\ -2 & -1\end{array}\right]$ $\newline$ A. It is Select an answer $0$ to compute $(A-5 B)^{T}$ because select an answer $\newline$ B. If the computation is possible, calculate $(A-5 B)^{T}$ . If the answer does not exist, enter DNE. $\newline$ Note: To enter a matrix, click inside the answer box and choose the

Full solution

Q. Question

12

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0 / 10

pts

\newline

5

\newline

98

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Details

\newline

Let

A=\left[\begin{array}{cc}-3 & -4 \\ 0 & 4 \\ -4 & -2\end{array}\right], B=\left[\begin{array}{cc}-4 & 0 \\ -3 & 0 \\ -2 & -1\end{array}\right]

\newline

A. It is Select an answer

0

to compute

(A-5 B)^{T}

because select an answer

\newline

B. If the computation is possible, calculate

(A-5 B)^{T}

. If the answer does not exist, enter DNE.

\newline

Note: To enter a matrix, click inside the answer box and choose the

Compute $5$ B: First, let's compute $5B$ . $\newline$ $B = \begin{bmatrix} -4 & 0 \\ -3 & 0 \\ -2 & -1 \end{bmatrix}$ $\newline$ $5B = 5 \times \begin{bmatrix} -4 & 0 \\ -3 & 0 \\ -2 & -1 \end{bmatrix} = \begin{bmatrix} -20 & 0 \\ -15 & 0 \\ -10 & -5 \end{bmatrix}$
Compute A - $5$ B: Next, compute $A - 5B$ . $\newline$ $A = \begin{bmatrix} -3 & -4 \\ 0 & 4 \\ -4 & -2 \end{bmatrix}$ $\newline$ $A - 5B = \begin{bmatrix} -3 & -4 \\ 0 & 4 \\ -4 & -2 \end{bmatrix} - \begin{bmatrix} -20 & 0 \\ -15 & 0 \\ -10 & -5 \end{bmatrix} = \begin{bmatrix} -3 - (-20) & -4 - 0 \\ 0 - (-15) & 4 - 0 \\ -4 - (-10) & -2 - (-5) \end{bmatrix}$ $\newline$ $A - 5B = \begin{bmatrix} 17 & -4 \\ 15 & 4 \\ 6 & 3 \end{bmatrix}$
Compute (A - $5$ B)^T: Now, compute the transpose $(A - 5B)^T$ . $\newline$ $(A - 5B)^T = \begin{bmatrix} 17 & -4 \\ 15 & 4 \\ 6 & 3 \end{bmatrix}^T = \begin{bmatrix} 17 & 15 & 6 \\ -4 & 4 & 3 \end{bmatrix}$