Question

\(\begin{bmatrix}13&15 \\ -1&4\end{bmatrix}\begin{bmatrix}2&0 \\ 0&2\end{bmatrix}=\ \ ?\)

• A. \(\begin{bmatrix}13&15 \\ -1&4\end{bmatrix}\)
• B. \(\begin{bmatrix}15&0 \\ 0&8\end{bmatrix}\)
• C. \(\begin{bmatrix}26&30 \\ -2&8\end{bmatrix}\)
• D. \(\begin{bmatrix}13&0 \\ 0&6\end{bmatrix}\)

Hint:

Multiplication by a diagonal matrix scales columns by the diagonal entries.

Answer 1

The Correct Option is C

Right matrix is \(2I\) (twice the identity). Multiplying any matrix by \(2I\) doubles each column: First column \( \to 2\times(13,-1)=(26,-2)\); second column \(\to 2\times(15,4)=(30,8)\). So product \(=\begin{bmatrix}26&30 \\ -2&8\end{bmatrix}\).