Question

Let the following system of equations

kx + y + z = 1

x + ky + z = k

x + y + kz = k²

has no solution. Find |k|

Options

• 0

• 1

• 2

• 3

Answer 1

2

Explanation:

`D = |(k, 1, 1),(1, k, 1),(1, 1, k)| = 0 ⇒ (k - 1)^2 (k + 2) = 0`

also `D_1 = |(1, 1, 1),(k, k, 1),(k^2, 1, k)| ≠ 0 ⇒ k ≠ 1 ⇒ k = -2`