Questions: Perform the operation if possible. 3[3 -1 -3; -4 3 -1; -3 -5 3] + 4[2 1 4; 4 2 6; 1 1 2] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 3[3 -1 -3; -4 3 -1; -3 -5 3] + 4[2 1 4; 4 2 6; 1 1 2] = □ (Type an integer or simplified fraction for each matrix element.) B. The operations are not defined.

$Perform the operation if possible. 3[3 -1 -3; -4 3 -1; -3 -5 3] + 4[2 1 4; 4 2 6; 1 1 2] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 3[3 -1 -3; -4 3 -1; -3 -5 3] + 4[2 1 4; 4 2 6; 1 1 2] = □ (Type an integer or simplified fraction for each matrix element.) B. The operations are not defined.$

Transcript text: 7 \& 8 Test Question 7 of 30 Perform the operation if possible. \[ 3\left[\begin{array}{rrr} 3 & -1 & -3 \\ -4 & 3 & -1 \\ -3 & -5 & 3 \end{array}\right]+4\left[\begin{array}{lll} 2 & 1 & 4 \\ 4 & 2 & 6 \\ 1 & 1 & 2 \end{array}\right] \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $3\left[\begin{array}{rrr}3 & -1 & -3 \\ -4 & 3 & -1 \\ -3 & -5 & 3\end{array}\right]+4\left[\begin{array}{lll}2 & 1 & 4 \\ 4 & 2 & 6 \\ 1 & 1 & 2\end{array}\right]=$ $\square$ (Type an integer or simplified fraction for each matrix element.) B. The operations are not defined.

Solution

Solution Steps

To solve this problem, we need to perform scalar multiplication on two matrices and then add the resulting matrices together. Specifically, we will multiply the first matrix by 3 and the second matrix by 4, and then add the corresponding elements of the two resulting matrices.

Step 1: Define the Matrices

We start with the following matrices: \[ A = \begin{bmatrix} 3 & -1 & -3 \\ -4 & 3 & -1 \\ -3 & -5 & 3 \end{bmatrix}, \quad B = \begin{bmatrix} 2 & 1 & 4 \\ 4 & 2 & 6 \\ 1 & 1 & 2 \end{bmatrix} \]

Step 2: Perform Scalar Multiplication

Next, we perform scalar multiplication on each matrix: \[ 3A = 3 \cdot \begin{bmatrix} 3 & -1 & -3 \\ -4 & 3 & -1 \\ -3 & -5 & 3 \end{bmatrix} = \begin{bmatrix} 9 & -3 & -9 \\ -12 & 9 & -3 \\ -9 & -15 & 9 \end{bmatrix} \] \[ 4B = 4 \cdot \begin{bmatrix} 2 & 1 & 4 \\ 4 & 2 & 6 \\ 1 & 1 & 2 \end{bmatrix} = \begin{bmatrix} 8 & 4 & 16 \\ 16 & 8 & 24 \\ 4 & 4 & 8 \end{bmatrix} \]

Step 3: Add the Resulting Matrices

Now, we add the two resulting matrices: \[ 3A + 4B = \begin{bmatrix} 9 & -3 & -9 \\ -12 & 9 & -3 \\ -9 & -15 & 9 \end{bmatrix} + \begin{bmatrix} 8 & 4 & 16 \\ 16 & 8 & 24 \\ 4 & 4 & 8 \end{bmatrix} = \begin{bmatrix} 17 & 1 & 7 \\ 4 & 17 & 21 \\ -5 & -11 & 17 \end{bmatrix} \]