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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 the values of x.
Solution
`|(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
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