Question

Find the value of a,b,c,d if \(\begin{bmatrix}a+b&c\\a-b&2c+d\end{bmatrix}\)=\(\begin{bmatrix}3&2\\1&6\end{bmatrix}\).

(a) 3, 2, 1, 4

(b) 3, 2, 1, 6

(c) 2, 2, 2, 2

(d) 2, 1, 2, 2

The question was asked during an interview for a job.

Origin of the question is Types of Matrices in section Matrices of Mathematics – Class 12

Answer 1

The correct choice is (d) 2, 1, 2, 2

To elaborate: The two matrices \(\begin{bmatrix}a+b&c\\a-b&2c+d\end{bmatrix}\)and\(\begin{bmatrix}3&2\\1&6\end{bmatrix}\) are equal matrices. Comparing the two matrices, we get

a-b=3, c=2, a-b=1, 2c+d=6

Solving the above equations, we get a=2, b=1, c=2, d=2.