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Answer the following question: By using properties of determinant prove that |x+yy+zz+xzxy111| = 0 - Mathematics and Statistics

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Question

Answer the following question:

By using properties of determinant prove that `|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)|` = 0

Sum
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Solution

L.H.S. = `|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)|`

By R1 + R2 , we get,

L.H.S. = `|(x + y + z, x + y + z, x + y + z),(z, x, y),(1, 1, 1)|`

By taking (x + y + z) common from R1, we get,

L.H.S. = `(x + y + z)|(1, 1, 1),(z, x, y),(1, 1, 1)|` 

=(x + y + z) × 0  ...[∵ R1 ≡ R3]

= 0

= R.H.S.

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Chapter 4: Determinants and Matrices - Miscellaneous Exercise 4(A) [Page 76]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) [English] Standard 11 Maharashtra State Board
Chapter 4 Determinants and Matrices
Miscellaneous Exercise 4(A) | Q II. (6) | Page 76

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