Question

For what value of k the system of equation x – ky + z = 0, kx + 3y - kz = 0, 3x + y - z = 0 have nontrivial solution *

Answer 1

Answer:

| 1 -k 1 |

| k 3 -k | = 0

| 3 1 -1 |

» (-3 + k) + k (-k + 3k) + 1 (k - 9) = 0

» - 3 + k + 2k² + k - 9 = 0

» 2k² + 2k - 12 = 0

» k² + k - 6 = 0

» k² + 3k - 2k - 6 = 0

» k (k + 3) - 2 (k + 3) = 0

» (k + 3) (k - 2) = 0

» k = -3 or 2

» k