Answer the following question: Without expanding determinant show that |lmnedfuvw|=|nfwlewmdv| - Mathematics and Statistics

Question

Answer the following question:

Without expanding determinant show that

`|(l, "m", "n"),("e", "d", "f"),("u", "v", "w")| = |("n", "f", "w"),(l, "e", "u"),("m", "d", "v")|`

Sum

Solution

L.H.S. = `|(l, "m", "n"),("e", "d", "f"),("u", "v", "w")|`

Interchanging rows and columns, we get

L.H.S. = `|(l, "e", "u"),("m", "d", "v"),("n", "f", "w")|`

Applying R₂ ↔ R₃, we get

L.H.S. = `-|(l, "e", "u"),("n", "f", "w"),("m", "d", "v")|`

Applying R₁ ↔ R₂, we get

L.H.S. = `|("n", "f", "w"),(l, "e", "u"),("m", "d", "v")|`

= R.H.S.

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Properties of Determinants

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Q II. (7) (iii)Q II. (7) (ii)Q II. (7) (iv)

Chapter 4: Determinants and Matrices - Miscellaneous Exercise 4(A) [Page 77]

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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. (7) (iii) | Page 77

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