Question

Multiply the matrices: \[ \left[ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right] \left[ \begin{matrix} 4 & 0 \\ 0 & 4 \end{matrix} \right] \]

• A. \( \left[ \begin{matrix} 4 & 8 \\ 0 & 16 \end{matrix} \right] \)
• B. \( \left[ \begin{matrix} 5 & 2 \\ 3 & 20 \end{matrix} \right] \)
• C. \( \left[ \begin{matrix} 4 & 8 \\ 12 & 16 \end{matrix} \right] \)
• D. \( \left[ \begin{matrix} 4 & 12 \\ 8 & 16 \end{matrix} \right] \)

Hint:

When multiplying two matrices, calculate the dot product of the rows from the first matrix and the columns from the second matrix.

Answer 1

The Correct Option is C

We are asked to multiply two matrices: \[ \left[ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right] \left[ \begin{matrix} 4 & 0 \\ 0 & 4 \end{matrix} \right] \] Performing the multiplication: - First row, first column: \[ 1 \times 4 + 2 \times 0 = 4 \] - First row, second column: \[ 1 \times 0 + 2 \times 4 = 8 \] - Second row, first column: \[ 3 \times 4 + 4 \times 0 = 12 \] - Second row, second column: \[ 3 \times 0 + 4 \times 4 = 16 \] Thus, the resulting matrix is: \[ \left[ \begin{matrix} 4 & 8
12 & 16 \end{matrix} \right] \]