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Example 13 - Chapter 4 Class 12 Determinants
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Example 13 Evaluate โ = 1๏ทฎ๐๏ทฎ๐๐๏ทฎ1๏ทฎ๐๏ทฎ๐๐๏ทฎ1๏ทฎ๐๏ทฎ๐๐๏ทฏ๏ทฏ โ = 1๏ทฎ๐๏ทฎ๐๐๏ทฎ1๏ทฎ๐๏ทฎ๐๐๏ทฎ1๏ทฎ๐๏ทฎ๐๐๏ทฏ๏ทฏ We need to obtain 0 in 2nd row as well as 3rd row Applying R2 โ R2 โ R1 โ = 1๏ทฎ๐๏ทฎ๐๐๏ทฎ๐ โ๐๏ทฎ๐โ๐๏ทฎ๐๐โ๐๐๏ทฎ1๏ทฎ๐๏ทฎ๐๐๏ทฏ๏ทฏ = 1๏ทฎ๐๏ทฎ๐๐๏ทฎ๐๏ทฎ๐โ๐๏ทฎ๐(๐โ๐)๏ทฎ1๏ทฎ๐๏ทฎ๐๐๏ทฏ๏ทฏ Applying R3 โ R3 โ R1 = 1๏ทฎ๐๏ทฎ๐๐๏ทฎ0๏ทฎ๐โ๐๏ทฎ๐(๐โ๐)๏ทฎ๐โ๐๏ทฎ๐โ๐๏ทฎ๐๐โ๐๐๏ทฏ๏ทฏ = 1๏ทฎ๐๏ทฎ๐๐๏ทฎ0๏ทฎ(๐โ๐)๏ทฎ๐(๐โ๐)๏ทฎ๐๏ทฎ(๐โ๐)๏ทฎ๐(๐โ๐)๏ทฏ๏ทฏ Expanding it along C1 = 1 ๐โ๐๏ทฏ๏ทฎ๐ ๐โ๐๏ทฏ๏ทฎ ๐โ๐๏ทฏ๏ทฎ๐ ๐โ๐๏ทฏ๏ทฏ๏ทฏโ0 ๐๏ทฎ๐๐๏ทฎ ๐โ๐๏ทฏ๏ทฎ๐ ๐โ๐๏ทฏ๏ทฏ๏ทฏ +0 ๐๏ทฎ๐๐๏ทฎ ๐โ๐๏ทฏ๏ทฎ๐ ๐โ๐๏ทฏ๏ทฏ๏ทฏ = 1 bโ๐๏ทฏ๏ทฎc ๐โ๐๏ทฏ๏ทฎ cโa๏ทฏ๏ทฎ๐ ๐โ๐๏ทฏ๏ทฏ๏ทฏ โ 0 + 0 = 1 (b โ a) b(a โ c) โ (c โ a) (c) (a โ b)๏ทฏ = โ(a โ b) b ( โ (c โ a)) โ (c โ a) c (a โ b) = (a โ b) b (c โ a) โ (c โ a) c (a โ b) = (a โ b)(c โ a) (b โ c)) = (a โ b) (b โ c) (c โ a) Thus โ = (a โ b) (b โ c) (c โ a)
Examples
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Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9 Important
Example 10 Important
Example 11
Example 12
Example 13 You are here
Example 14 Important
Example 15 Important
Example 16 Important
Example 17
Example 18 Important
Example 19
Example 20
Example 21
Example 22
Example 23
Example 24 Important
Example 25
Example 26 Important
Example 27
Example 28 Important
Example 29
Example 30
Example 31 Important
Example 32 Important
Example 33 Important
Example 34 Important
Chapter 4 Class 12 Determinants
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About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.