Question

If A = \(\begin{bmatrix}3&4\\1&2\end{bmatrix}\)  and B = \(\begin{bmatrix}1&5\\2&3\end{bmatrix}\), find 2A-3B.

(a) \(\begin{bmatrix}3&7\\-4&5\end{bmatrix}\)

(b) \(\begin{bmatrix}-3&-7\\-4&-5\end{bmatrix}\)

(c) \(\begin{bmatrix}3&7\\-4&-5\end{bmatrix}\)

(d) \(\begin{bmatrix}3&-7\\-4&-5\end{bmatrix}\)

This question was posed to me in an online interview.

This intriguing question comes from Operations on Matrices in chapter Matrices of Mathematics – Class 12

Answer 1

The correct choice is (d) \(\begin{bmatrix}3&-7\\-4&-5\end{bmatrix}\)

To elaborate: Given that, A = \(\begin{bmatrix}3&4\\1&2\end{bmatrix}\)  and B = \(\begin{bmatrix}1&5\\2&3\end{bmatrix}\)

⇒2A=2\(\begin{bmatrix}3&4\\1&2\end{bmatrix}\)=\(\begin{bmatrix}6&8\\2&4\end{bmatrix}\) and 3B=3\(\begin{bmatrix}1&5\\2&3\end{bmatrix}\)=\(\begin{bmatrix}3&15\\6&9\end{bmatrix}\)

∴2A-3B = \(\begin{bmatrix}6&8\\2&4\end{bmatrix}\)–\(\begin{bmatrix}3&15\\6&9\end{bmatrix}\)=\(\begin{bmatrix}3&-7\\-4&-5\end{bmatrix}\).