Question

Find the value of x and y if 2\(\begin{bmatrix}5&x\\y-4&6\end{bmatrix}\)+\(\begin{bmatrix}-4&1\\3&2\end{bmatrix}\)=\(\begin{bmatrix}6&3\\10&14\end{bmatrix}\)?

(a) x=-1, y=9

(b) x=-1, y=-9

(c) x=1, y=-9

(d) x=1, y=9

I had been asked this question in exam.

The doubt is from Operations on Matrices topic in portion Matrices of Mathematics – Class 12

Answer 1

The correct answer is (d) x=1, y=9

Explanation: Given that, 2\(\begin{bmatrix}5&x\\y-4&6\end{bmatrix}\)+\(\begin{bmatrix}-4&1\\3&2\end{bmatrix}\)=\(\begin{bmatrix}6&3\\10&14\end{bmatrix}\)

⇒\(\begin{bmatrix}2(5)-4&2x+1\\2(y-4)+3&2(6)+2\end{bmatrix}\)=\(\begin{bmatrix}6&3\\10&14\end{bmatrix}\)

Comparing the two matrices, 2x+1=3, 2y-8=10

Solving the two equations we get, x=1, y=9.