Question

\(\begin{bmatrix}2&3 \\ 5&7\end{bmatrix}\!\begin{bmatrix}2 \\ 5\end{bmatrix}=\ \ ?\)

• A. \(\begin{bmatrix}4 \\ 25\end{bmatrix}\)
• B. \(\begin{bmatrix}4 \\ 10 \\ 35\end{bmatrix}\)
• C. \(\begin{bmatrix}19 \\ 45\end{bmatrix}\)
• D. \(\begin{bmatrix}19 \\ 45\end{bmatrix}\)

Hint:

\((2\times2)(2\times1)\Rightarrow(2\times1)\) — size check prevents mistakes.

Answer 1

The Correct Option is D

Row–column rule: Top entry \(=2\cdot2+3\cdot5=4+15=19\). Bottom entry \(=5\cdot2+7\cdot5=10+35=45\).