Question

Find  a,b,c,d if \(\begin{bmatrix}a&b+c\\c+d&b\end{bmatrix}\)=\(\begin{bmatrix}3&2\\3&-1\end{bmatrix}\) are equal matrices.

(a) 3, 0, 1, -1

(b) 1,-3, 0, 3

(c) 3, -1, 3, 0

(d) 3, 3, -1, -1

I got this question during an internship interview.

I'd like to ask this question from Types of Matrices topic in portion Matrices of Mathematics – Class 12

Answer 1

Right answer is (c) 3, -1, 3, 0

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

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

Solving the above equations, we get a=3, b=-1, c=3, d=0.