Question

If A = `[(1,2,3),(2,"a",2),(5,7,3)]` is a singular matrix , find the value of 'a'.

Answer 1

∵ A is a singular matrix.

|A| = 0

`|(1,2,3),(2,"a",2),(5,7,3)|`

`= 1 xx |("a",2),(7,3)| - 2  |(2,2),(5,3)| + 3  |(2,"a"),(5,7)|`

= (3a - 14) - 2 (-4) + 3 (14 - 5a) 

= 36 - 12a

∴ 36 - 12a = 0 

⇒ a = 3