Question

Multiply the matrices: \[ \left[ \begin{matrix} 2 & 5 \\ 3 & 7 \end{matrix} \right] \left[ \begin{matrix} 2 & 5 \end{matrix} \right] \] \\

• A. \( \left[ \begin{matrix} 4 & 25 \\ 6 & 35 \end{matrix} \right]\)
• B. \( \left[ \begin{matrix} 4 & 15 \\10 & 35 \end{matrix} \right]\)
• C. \( \left[ \begin{matrix} 19 & 45 \end{matrix} \right]\)
• D. \( \left[ \begin{matrix} 19 & 45 \end{matrix} \right] \)

Hint:

When multiplying a matrix by a vector, treat the vector as a column matrix and calculate the dot products of each row with the vector.

Answer 1

The Correct Option is D

The given matrix multiplication involves multiplying: \[ \left[ \begin{matrix} 2 & 5 \\ 3 & 7 \end{matrix} \right] \left[ \begin{matrix} 2 \\ 5 \end{matrix} \right] \] The product will result in a single element, since we are multiplying a 2x2 matrix with a 2x1 matrix: \[ 2 \times 2 + 5 \times 5 = 4 + 25 = 29 \] Thus, the resulting matrix is: \[ \left[ \begin{matrix} 19 & 45 \end{matrix} \right] \]