Question

Find the matrix M and N, if M+N = \(\begin{bmatrix}5&6\\7&8\end{bmatrix}\),M-N = \(\begin{bmatrix}4&5\\6&8\end{bmatrix}\).

(a) M=1/2 \(\begin{bmatrix}9&11\\13&16\end{bmatrix}\), N=1/2 \(\begin{bmatrix}1&1\\1&0\end{bmatrix}\)

(b) M=\(\begin{bmatrix}5&6\\7&8\end{bmatrix}\), N=\(\begin{bmatrix}4&5\\8&6\end{bmatrix}\)

(c) M=1/2 \(\begin{bmatrix}9&2\\13&16\end{bmatrix}\), N=1/2 \(\begin{bmatrix}1&1\\2&5\end{bmatrix}\)

(d) M=1/2 \(\begin{bmatrix}4&5\\1&2\end{bmatrix}\), N=1/2 \(\begin{bmatrix}1&2\\1&2\end{bmatrix}\)

I have been asked this question by my school teacher while I was bunking the class.

My question is from Operations on Matrices topic in portion Matrices of Mathematics – Class 12

Answer 1

The correct choice is (a) M=1/2 \(\begin{bmatrix}9&11\\13&16\end{bmatrix}\), N=1/2 \(\begin{bmatrix}1&1\\1&0\end{bmatrix}\)

For explanation I would say: M+N = \(\begin{bmatrix}5&6\\7&8\end{bmatrix}\)-(1) and M-N = \(\begin{bmatrix}4&5\\6&8\end{bmatrix}\)-(2)

Adding equation (1) and equation (2), (M+N)+(M-N)=2M=\(\begin{bmatrix}5&6\\7&8\end{bmatrix}\)+\(\begin{bmatrix}4&5\\6&8\end{bmatrix}\)

M=1/2 \(\begin{bmatrix}9&11\\13&16\end{bmatrix}\).

Subtracting equation (1) and equation (2), (M+N)-(M-N)=2N=\(\begin{bmatrix}5&6\\7&8\end{bmatrix}\)–\(\begin{bmatrix}4&5\\6&8\end{bmatrix}\)

N=1/2 \(\begin{bmatrix}1&1\\1&0\end{bmatrix}\).