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Question
If `[(4 - x, 4 + x, 4 + x),(4 + x, 4 - x, 4 + x),(4 + x, 4 + x, 4 - x)]` = 0, then find values of x.
Solution
We have, `|(4 - x, 4 + x, 4 + x),(4 + x, 4 - x, 4 + x),(4 + x, 4 + x, 4 - x)|` = 0
[Applying R1 → R1 + R2 + R3]
⇒ `|(12 + x, 12 + x, 12 + x),(4 + x, 4 - x, 4 + x),(4 + x, 4 + x, 4 - x)|` = 0
[Taking (12 + x) common from R1]
⇒ `(12 + x)|(1, 1, 1),(4 + x, 4 - x, 4 + x),(4 + x, 4 + x, 4 - x)|` = 0
[Applying C1 → C1 – C2 and C2 → C2 – C3]
⇒ `(12 + x)|(0, 0, 1),(0, -2x, 4 + x),(2x, 2x, 4 - x)|` = 0
⇒ `(12 + x)(0 - (-2x)(2x)]` = 0
⇒ `(12 + x)(4x^2)` = 0
∴ x = –12, 0
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