Question

The existence of unique solution of the system of linear equations x + y + z = a, 5x – y + bz = 10, 2x + 3y – z = 6 depends on 

Options

• a only

• b only

• a but not b

• a and b both

Answer 1

b only

Explanation:

Given system of linear equations have unique solution.

∴ Only `|A| ≠ 0 ⇒ |(1, 1, 1),(5, -1, b),(2, 3, -1)| ≠ 0`

⇒ `1(1 - 3b) - 1(-5 - 2b) + 1(15 + 2) ≠ 0`

⇒ `b ≠ - 23`

So, depends on b only.