Question

Find the product of the matrices: \[ \left[ \begin{matrix} 3 & -2 \\ -1 & -1 \end{matrix} \right] \]

• A. \( \left[ \begin{matrix} 3 & 2 \end{matrix} \right]\)
• B. \( \left[ \begin{matrix} 3 & 2 \end{matrix} \right]\)
• C. \( \left[ \begin{matrix} 1 & 1 \end{matrix} \right]\)\)
• D. \( \left[ \begin{matrix} 5 \end{matrix} \right] \)

Hint:

When performing matrix multiplication, ensure that you multiply corresponding elements of rows and columns and sum them.

Answer 1

The Correct Option is D

We are given the matrix multiplication: \[ \left[ \begin{matrix} 3 & -2 \\ -1 & -1 \end{matrix} \right] \] We perform the matrix multiplication to find the result. The product of a 2x2 matrix by another 2x2 matrix is calculated by taking the sum of the products of corresponding elements from each row and column: - \( (3 \times 1) + (-2 \times 1) = 3 - 2 = 1 \) - \( (-1 \times 1) + (-1 \times 1) = -1 - 1 = -2 \) Thus, the resulting matrix is: \[ \left[ \begin{matrix} 1 & -2 \end{matrix} \right] \] (D) is the correct answer.