Questions: Find the following matrix product, if it exists. [-3 9 7; 4 0 6; -9 -1 -4][5 -1; 1 0; 8 -7] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. [-3 9 7; 4 0 6; -9 -1 -4][5 -1; 1 0; 8 -7]= (Simplify your answer.) B. The product does not exist.

Find the following matrix product, if it exists.
[-3 9 7; 4 0 6; -9 -1 -4][5 -1; 1 0; 8 -7]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. [-3 9 7; 4 0 6; -9 -1 -4][5 -1; 1 0; 8 -7]= (Simplify your answer.)
B. The product does not exist.

Transcript text: Find the following matrix product, if it exists. \[ \left[\begin{array}{rrr} -3 & 9 & 7 \\ 4 & 0 & 6 \\ -9 & -1 & -4 \end{array}\right]\left[\begin{array}{rr} 5 & -1 \\ 1 & 0 \\ 8 & -7 \end{array}\right] \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\left[\begin{array}{rrr}-3 & 9 & 7 \\ 4 & 0 & 6 \\ -9 & -1 & -4\end{array}\right]\left[\begin{array}{rr}5 & -1 \\ 1 & 0 \\ 8 & -7\end{array}\right]=\square$ (Simplify your answer.) B. The product does not exist.

Solution

Solution Steps

Step 1: Verify Multiplication Possibility

To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. In this case, the number of columns in matrix A is 3 and the number of rows in matrix B is 3, which match, so multiplication is possible.

Step 2: Initialize the Result Matrix C

The result matrix C will have dimensions 3 x 2, initialized with zeros.

Step 3: Compute Each Element of C

Each element $c_{ij}$ in $C$ is computed as the dot product of the $i$-th row of $A$ and the $j$-th column of $B$: $$c_{ij} = \sum_{k=1}^{n} a_{ik}b_{kj}$$ Where $n$ is the common dimension of matrices $A$ and $B$.