Question

If A = `|(3,-2),(-1 , 4)|` , B = `|(2"a"),(1)|` , C = `|(-4),(5)|` , D = `|(2),("b")|` and AB + 2C = 4D then find the values of a and b.

Answer 1

A = `|(3,-2),(-1 , 4)|_(2 xx 2)` , B = `|(2"a"),(1)|_(2 xx 1)`

C = `|(-4),(5)|_(2 xx 1)` , D = `|(2),("b")|_(2 xx 1)`

AB = `|(3,-2),(-1 , 4)|  |(2"a"),(1)|` 

`= |(6"a" - 2),(-2"a" + 4)|_(2 xx 1)`

2C = `|(-8),(10)|`

AB + 2C = `|(6"a" - 2),(-2"a" + 4)|  |(-8),(10)|`

`= |(6"a" - 10),(-2"a" + 14)|_(2 xx 1)`

4D = `|(8),(4"b")|`

Given, AB + 2C = 4D

`|(6"a" - 10),(-2"a" + 14)| = |(8) , (4"b")|` 

6a - 10 = 8

⇒  6a=18 

⇒ a = 3

- 2a + 14 = 4b

⇒   -2(3 )+ 14 =4 b 

⇒ 8 = 4 b

⇒ 2 = b