Maharashtra State BoardHSC Science (General) 11th
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Answer the following question: Without expanding determinant show that |lmnedfuvw|=|nfwlewmdv| - Mathematics and Statistics

Sum

Answer the following question:

Without expanding determinant show that

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

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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", "w"),("m", "d", "v")|`

= R.H.S.

  Is there an error in this question or solution?
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Determinants and Matrices
Miscellaneous Exercise 4(A) | Q II. (7) (iii) | Page 77
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