Question

If `|(4 + x, 4 - x, 4 - x),(4 - x, 4 + x, 4 - x),(4 - x, 4 - x, 4 + x)|` = 0, then find the values of x.

Answer 1

`|(4 + x, 4 - x, 4 - x),(4 - x, 4 + x, 4 - x),(4 - x, 4 - x, 4 + x)|` = 0

Applying C₁ → C₁ + C₂ + C₃, we get

`|(12 -  x, 4 - x, 4 - x),(12 -  x, 4 + x, 4 - x),(12 -  x, 4 - x, 4 + x)|` = 0

Taking (12 – x) common from C₁, we get

`(12 - x) |(1, 4 - x, 4 - x),(1, 4 + x, 4 - x),(1, 4 - x, 4 + x)|` = 0

Applying R₂ → R₂ – R₁ and R₃ → R₃ – R₁, we get

`(12 - x) |(1, 4 - x, 4 - x),(0, 2x, 0),(0, 0, 2x)|` = 0

∴ (12 – x)[1(4x² – 0) –(4 – x)(0 – 0) + (4 –x)(0 – 0)] = 0
∴ (12 –x)(4x²) = 0
∴ x²(12 – x) = 0
∴ x = 0 or 12 – x = 0
∴ x = 0 or x = 12