Question

If $\left[\begin{array}{cc}a+b& 2\\ 5& ab\end{array}\right]=\left[\begin{array}{cc}6& 2\\ 5& 8\end{array}\right]$ , find the values of a and b.

Answer 1

By comparing corresponding elements of both the matrices, we get

a + b = 6 ……………………. (1)

ab = 8 ……………………….. (2)

a + b = 6 $\to$ a = 6 – b …… (3)

Substitute (3) in (2)

(6 – b)b = 8

$\to$6b – $b^2$ – 8 = 0

$\to$ $b^2$ – 6b + 8 = 0

$\to$ (b – 4)(b – 2) = 0

b = 4, 2

So a + b = 6

When b = 4

a = 6 – 4 = 2

When b = 2

a = 6 - 2 = 4

Therefore a = 2, 4 and b = 4, 2