Question

Which of the following matrices are singular or non singular?

`[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`

Answer 1

Let A = `[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`

∴ |A| = `|("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")|`

Applying R₃ → R₃ + R₂, we get

|A| = `|("a", "b", "c"),("p", "q", "r"),(2"a", 2"b", 2"c")|`

Taking 2 common from R₃, we get

|A| = `2|("a", "b", "c"),("p", "q", "r"),("a", "b", "c")|`

= 2(0)       ...[∵ R1 and R3 are identical]
= 0
∴ A is a singular martix.