Question

If A = \(\begin{bmatrix}1&2&3\\9&10&11\end{bmatrix}\) and B = \(\begin{bmatrix}0&5&0\\5&0&5\end{bmatrix}\), then find A+B.

(a) A+B = \(\begin{bmatrix}1&7&3\\11&10&16\end{bmatrix}\)

(b) A+B = \(\begin{bmatrix}1&7&3\\14&11&13\end{bmatrix}\)

(c) A+B = \(\begin{bmatrix}1&7&3\\14&10&16\end{bmatrix}\)

(d) A+B = \(\begin{bmatrix}1&5&3\\14&10&16\end{bmatrix}\)

I had been asked this question by my college professor while I was bunking the class.

This is a very interesting question from Operations on Matrices in division Matrices of Mathematics – Class 12

Answer 1

The correct answer is (c) A+B = \(\begin{bmatrix}1&7&3\\14&10&16\end{bmatrix}\)

Explanation: Given that, A = \(\begin{bmatrix}1&2&3\\9&10&11\end{bmatrix}\) and B = \(\begin{bmatrix}0&5&0\\5&0&5\end{bmatrix}\)

Then A+B = \(\begin{bmatrix}1+0&2+5&3+0\\9+5&10+0&11+5\end{bmatrix}\) = \(\begin{bmatrix}1&7&3\\14&10&16\end{bmatrix}\).