Find values of a and b if A = B,

Question:

Find values of a and b if A = B, where

$\mathrm{A}=\left[\begin{array}{cc}a+4 & 3 b \\ 8 & -6\end{array}\right], \quad \mathrm{B}=\left[\begin{array}{cc}2 a+2 & b^{2}+2 \\ 8 & b^{2}-5 b\end{array}\right]$

Solution:

Given, matrix A = matrix B

Then their corresponding elements are equal.

So, we have

a11 = b11; a + 4 = 2a + 2 ⇒ a = 2

a12 = b12; 3b = b2 + 2 ⇒ b2 – 3b + 2 = 0 ⇒ b = 1, 2

a22 = b22; -6 = b2 – 5b ⇒ b2 – 5b + 6 = 0 ⇒ b = 2, 3

Hence, a = 2 and b = 2 (common value)

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