Question

The value of k for which the system of equations x + ky + 3z = 0, 4x + 3y + kz = 0, 2x + y + 2z = 0 has nontrivial solution is

Options

• k = 0 or `9/2`

• k = 10

• k < 9

• k > 0

Answer 1

k = 0 or `9/2`

Explanation:

Given that system of equation has non-trivial solution

∴ `|(1, k, 3),(4, 3, k),(2, 1, 2)| = 0`

⇒ 1(6 – k) – k(8 – 2k) + 3(4 – 6) = 0

⇒ 6 – k – 8k + 2k² – 6 = 0

⇒ 2k² – 9k = 0

⇒ k = 0 or k = `9/2`