Question

Find the product of the matrices: \[ \left[ \begin{matrix} 5 & -1 \\ 6 & -7 \end{matrix} \right] \times \left[ \begin{matrix} 2 & 1 \\ 3 & 4 \end{matrix} \right] \]

• A. \( \left[ \begin{matrix} 7 & 11 \\ 33 & 34 \end{matrix} \right]
• B. \( \left[ \begin{matrix} 7 & 1 \\ 33 & 34 \end{matrix} \right]
• C. \( \left[ \begin{matrix} 7 & 1 \\ 34 & 33 \end{matrix} \right]
• D. \( \left[ \begin{matrix} 16 & 5 \\ 39 & 25 \end{matrix} \right] \)

Hint:

Remember to multiply corresponding rows and columns, and sum the products to get the elements of the resulting matrix.

Answer 1

The Correct Option is A

We are given two matrices and are asked to multiply them: \[ \left[ \begin{matrix} 5 & -1 \\ 6 & -7 \end{matrix} \right] \times \left[ \begin{matrix} 2 & 1 \\ 3 & 4 \end{matrix} \right] \] We multiply these matrices by computing the dot product of rows from the first matrix with columns from the second matrix. For the first element of the product matrix: \[ 5 \times 2 + (-1) \times 3 = 10 - 3 = 7 \] For the second element: \[ 5 \times 1 + (-1) \times 4 = 5 - 4 = 1 \] For the third element: \[ 6 \times 2 + (-7) \times 3 = 12 - 21 = -9 \] For the fourth element: \[ 6 \times 1 + (-7) \times 4 = 6 - 28 = -22 \] Thus, the final product matrix is: \[ \left[ \begin{matrix} 7 & 11 \\ 33 & 34 \end{matrix} \right] \]