Question

Find the values of a and b) if [2a + 3b a - b] = [19  2]. 

Answer 1

[2a+3b  a-b] = [19  2] 

[2a+3b   a-b]  is 1 x 2 matrix  and [19   2] is 1 x 2 matrix 

2a + 3b = 19  ......(1) 

a - b = 2   ......(2)

⇒  a = 2 + b 

Putting the value of a in equation (1) 

4 + 2b + 3b = 19  .... (1)

⇒  5b= 15 

⇒  b = 3 

From (2) 

a = 2+3 = 5