Maharashtra State BoardHSC Arts 11th
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If |4+x4-x4-x4-x4+x4-x4-x4-x4+x| = 0, then find the values of x. - Mathematics and Statistics

Sum

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.

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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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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Determinants and Matrices
Exercise 4.2 | Q 5 | Page 68
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