Question

If A+B = \(\begin{bmatrix}6&7\\5&0\end{bmatrix}\)and A = \(\begin{bmatrix}2&5\\1&-1\end{bmatrix}\). Find the matrix B.

(a) B = \(\begin{bmatrix}4&1\\2&4\end{bmatrix}\)

(b) B = \(\begin{bmatrix}4&2\\4&1\end{bmatrix}\)

(c) B = \(\begin{bmatrix}4&1\\4&2\end{bmatrix}\)

(d) B = \(\begin{bmatrix}4&4\\4&2\end{bmatrix}\)

I had been asked this question in my homework.

My question is taken from Operations on Matrices in section Matrices of Mathematics – Class 12

Answer 1

The correct answer is (b) B = \(\begin{bmatrix}4&2\\4&1\end{bmatrix}\)

Best explanation: Given that, A+B = \(\begin{bmatrix}6&7\\5&0\end{bmatrix}\)and A = \(\begin{bmatrix}2&5\\1&-1\end{bmatrix}\)

⇒B=(A+B)-A = \(\begin{bmatrix}6&7\\5&0\end{bmatrix}\)–\(\begin{bmatrix}2&5\\1&-1\end{bmatrix}\)

B = \(\begin{bmatrix}4&2\\4&1\end{bmatrix}\)