Question

Identify the singular and non-singular matrices:

`[(0, "a" - "b", "k"),("b" - "a", 0, 5),(-"k", -5, 0)]`

Answer 1

Let C = `[(0, "a" - "b", "k"),("b" - "a", 0, 5),(-"k", -5, 0)]`

|C| = `|(0, "a" - "b", "k"),("b" - "a", 0, 5),(-"k", -5, 0)|`

|C| = 0 – (a – b) (0 + 5k) + k(– 5(b – a) – 0)

|C| =  – 5k(a – b) – 5k(b – a)

|C| =  – 5k(a – b) + 5k(a – b)

|C| = 0

∴ C is a singular matrix.