Question

Evaluate the following matrix multiplication: \[ \begin{pmatrix} -3 & 5 & 2 \end{pmatrix} \times \begin{pmatrix} 1 \\ 6 \\ -4 \end{pmatrix} \]

• A. \(\begin{pmatrix} -18 & 30 & 12 \\ 12 & -20 & -8 \end{pmatrix}\)
• B. \(\begin{pmatrix} -18 & 5 & -20 \\ 12 & 30 & -8 \end{pmatrix}\)
• C. \(\begin{pmatrix} 30 & -18 & 12 \\ -20 & 12 & -8 \end{pmatrix}\)
• D. \(\begin{pmatrix} 18 & 30 & 12 \\ 12 & 20 & 8 \end{pmatrix}\)

Hint:

To multiply a row matrix with a column matrix, simply multiply corresponding elements and sum them up.

Answer 1

The Correct Option is A

We are given two matrices: \[ \text{Matrix 1: } \begin{pmatrix} -3 & 5 & 2 \end{pmatrix}, \quad \text{Matrix 2: } \begin{pmatrix} 1 \\ 6 \\ -4 \end{pmatrix} \] To multiply a row matrix with a column matrix, we multiply each corresponding element and then sum the products: \[ \text{Result} = (-3)(1) + (5)(6) + (2)(-4) = -3 + 30 - 8 = 19 \] Thus, the resulting matrix is: \[ \begin{pmatrix} -18 & 30 & 12 \\ 12 & -20 & -8 \end{pmatrix} \]