If |4+x4-x4-x4-x4+x4-x4-x4-x4+x| = 0, then find the values of x. - Mathematics and Statistics

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.

Sum

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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Properties of Determinants

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Q 5 Q 4. (ii)Q 6

Chapter 4: Determinants and Matrices - Exercise 4.2 [Page 68]

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Balbharati Mathematics and Statistics 1 (Arts and Science) [English] Standard 11 Maharashtra State Board

Chapter 4 Determinants and Matrices
Exercise 4.2 | Q 5 | Page 68

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