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Ex 4.2, 4 - Using property of determinants |1 bc a(b + c)| - Two rows or columns same

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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise
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Ex 4.2, 4 Using the property of determinants and without expanding, prove that: 1๏ทฎ๐‘๐‘๏ทฎ๐‘Ž(๐‘+๐‘)๏ทฎ1๏ทฎ๐‘๐‘Ž๏ทฎ๐‘(๐‘+๐‘Ž)๏ทฎ1๏ทฎ๐‘Ž๐‘๏ทฎ๐‘(๐‘Ž+๐‘)๏ทฏ๏ทฏ = 0 1๏ทฎ๐‘๐‘๏ทฎ๐‘Ž(๐‘+๐‘)๏ทฎ1๏ทฎ๐‘๐‘Ž๏ทฎ๐‘(๐‘+๐‘Ž)๏ทฎ1๏ทฎ๐‘Ž๐‘๏ทฎ๐‘(๐‘Ž+๐‘)๏ทฏ๏ทฏ = 1๏ทฎ๐‘๐‘๏ทฎ๐‘Ž๐‘+๐‘Ž๐‘๏ทฎ1๏ทฎ๐‘๐‘Ž๏ทฎ๐‘๐‘+๐‘๐‘Ž๏ทฎ1๏ทฎ๐‘Ž๐‘๏ทฎ๐‘๐‘Ž+๐‘๐‘๏ทฏ๏ทฏ C3 โ†’ C3 + C2 = 1๏ทฎ๐‘๐‘๏ทฎ๐‘Ž๐‘+๐‘Ž๐‘+๐‘๐‘๏ทฎ1๏ทฎ๐‘๐‘Ž๏ทฎ๐‘๐‘+๐‘๐‘Ž+๐‘๐‘๏ทฎ1๏ทฎ๐‘Ž๐‘๏ทฎ๐‘๐‘Ž+๐‘๐‘+๐‘๐‘๏ทฏ๏ทฏ = 1๏ทฎ๐‘๐‘๏ทฎ๐‘Ž๐‘+๐‘Ž๐‘+๐‘๐‘๏ทฎ1๏ทฎ๐‘๐‘Ž๏ทฎ๐‘๐‘+๐‘๐‘Ž+๐‘๐‘๏ทฎ1๏ทฎ๐‘Ž๐‘๏ทฎ๐‘๐‘Ž+๐‘๐‘+๐‘๐‘๏ทฏ๏ทฏ = (๐‘Ž๐‘+๐‘Ž๐‘+๐‘๐‘) 1๏ทฎ๐‘๐‘๏ทฎ1๏ทฎ1๏ทฎ๐‘๐‘Ž๏ทฎ1๏ทฎ1๏ทฎ๐‘Ž๐‘๏ทฎ1๏ทฏ๏ทฏ C1 and C3 is same = 0

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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