Question

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

• A. \( \left[ \begin{matrix} -6 \\ 5 \end{matrix} \right] \)
• B. \( \left[ \begin{matrix} -6 \\ 5 \end{matrix} \right] \)
• C. \( \left[ \begin{matrix} -1 \end{matrix} \right]\)
• D. \( \left[ \begin{matrix} 1 \end{matrix} \right] \)

Hint:

When multiplying a row matrix by a column matrix, the result is a scalar that is the dot product of the row and column.

Answer 1

The Correct Option is C

We are given two matrices and are asked to multiply them: \[ \left[ \begin{matrix} 6 & 5 \end{matrix} \right] \left[ \begin{matrix} -1 \\ 1 \end{matrix} \right] \] This multiplication involves calculating the dot product of the row vector and the column vector. The result will be a scalar: \[ 6 \times (-1) + 5 \times 1 = -6 + 5 = -1 \] Thus, the result is: \[ \left[ \begin{matrix} -1 \end{matrix} \right] \]