Find the Folliving matrices where \( A=\left[\begin{array}{rr}6 & -7 \\ -4 & 6 \\ -1 & 4\end{array}\right] \) and \( B=\left[\begin{array}{cc}-9 & 8 \\ 3 & 0 \\ -3 & 8\end{array}\right] \) Select the correct chace below O. A. \( 3 A-9 B=\square \) simplify your ansmer O B. This matrix openation is not passt

To find the matrix \( 3A - 9B \), we first need to calculate \( 3A \) and \( 9B \) separately. Given: \[ A = \begin{bmatrix} 6 & -7 \\ -4 & 6 \\ -1 & 4 \end{bmatrix} \] \[ B = \begin{bmatrix} -9 & 8 \\ 3 & 0 \\ -3 & 8 \end{bmatrix} \] ### Step 1: Calculate \( 3A \) \[ 3A = 3 \cdot \begin{bmatrix} 6 & -7 \\ -4 & 6 \\ -1 & 4 \end{bmatrix} = \begin{bmatrix} 3 \cdot 6 & 3 \cdot -7 \\ 3 \cdot -4 & 3 \cdot 6 \\ 3 \cdot -1 & 3 \cdot 4 \end{bmatrix} = \begin{bmatrix} 18 & -21 \\ -12 & 18 \\ -3 & 12 \end{bmatrix} \] ### Step 2: Calculate \( 9B \) \[ 9B = 9 \cdot \begin{bmatrix} -9 & 8 \\ 3 & 0 \\ -3 & 8 \end{bmatrix} = \begin{bmatrix} 9 \cdot -9 & 9 \cdot 8 \\ 9 \cdot 3 & 9 \cdot 0 \\ 9 \cdot -3 & 9 \cdot 8 \end{bmatrix} = \begin{bmatrix} -81 & 72 \\ 27 & 0 \\ -27 & 72 \end{bmatrix} \] ### Step 3: Calculate \( 3A - 9B \) Now we can subtract \( 9B \) from \( 3A \): \[ 3A - 9B = \begin{bmatrix} 18 & -21 \\ -12 & 18 \\ -3 & 12 \end{bmatrix} - \begin{bmatrix} -81 & 72 \\ 27 & 0 \\ -27 & 72 \end{bmatrix} \] To perform the subtraction, we subtract corresponding elements: \[ = \begin{bmatrix} 18 - (-81) & -21 - 72 \\ -12 - 27 & 18 - 0 \\ -3 - (-27) & 12 - 72 \end{bmatrix} \] \[ = \begin{bmatrix} 18 + 81 & -21 - 72 \\ -12 - 27 & 18 - 0 \\ -3 + 27 & 12 - 72 \end{bmatrix} \] \[ = \begin{bmatrix} 99 & -93 \\ -39 & 18 \\ 24 & -60 \end{bmatrix} \] ### Final Result Thus, the result of \( 3A - 9B \) is: \[ \begin{bmatrix} 99 & -93 \\ -39 & 18 \\ 24 & -60 \end{bmatrix} \] So the correct choice is: **A. \( 3A - 9B = \begin{bmatrix} 99 & -93 \\ -39 & 18 \\ 24 & -60 \end{bmatrix} \)**.