Question

Multiply the matrix: \[ \left[ \begin{matrix} 4 & -2 \\ \end{matrix} \right] \] \[ \left[ \begin{matrix} -1 \\ -1 \end{matrix} \right] \]

• A. \( \left[ \begin{matrix} -8 & -8 \end{matrix} \right]\)
• B. \( \left[ \begin{matrix} 0 \end{matrix} \right]\)
• C. \( \left[ \begin{matrix} -8 \end{matrix} \right]\)
• D. \( \left[ \begin{matrix} 6 & 2 \end{matrix} \right] \)

Hint:

When multiplying a row vector with a column vector, take the dot product of the row and column vectors.

Answer 1

The Correct Option is A

We are multiplying two matrices: \[ \left[ \begin{matrix} 4 & -2 \end{matrix} \right] \left[ \begin{matrix} -1 \\ -1 \end{matrix} \right] \] Matrix multiplication involves multiplying corresponding elements and summing them. The result is a 1x1 matrix: \[ (4 \times -1) + (-2 \times -1) = -4 + 2 = -2 \] Therefore, the correct answer is \( \left[ \begin{matrix} -8 & -8 \end{matrix} \right] \).