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Question
Solve the following equation:
`|(x + 2, x + 6, x - 1),(x + 6, x - 1, x + 2),(x - 1, x + 2, x + 6)|` = 0
Solution
`|(x + 2, x + 6, x - 1),(x + 6, x - 1, x + 2),(x - 1, x + 2, x + 6)|` = 0
By R2 – R1 and R3 – R1, we get,
`|(x + 2, x + 6, x - 1),(4, -7, 3),(-3, -4, 7)|` = 0
By C2 – C1 and C3 – C1, we get,
`|(x + 2, 4, -3),(4, -11, -1),(-3, -1, 10)|` = 0
∴ (x + 2)( –110 – 1) – 4 (40 – 3) – 3 ( –4 – 33) = 0
∴ (x + 2)( – 111) – 4 (37) – 3 ( – 37) = 0
∴ 37[ –3(x + 2) – 4 – 3( – 1)] = 0
∴ – 3 (x + 2) – 4 + 3 = 0
∴ – 3x – 6 – 1 = 0
∴ – 3x = 7
∴ x = `-7/3`.
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