1. Chapter 4 Class 12 Determinants
  2. Serial order wise


Ex 4.2, 4 Using the property of determinants and without expanding, prove that: |โ– 8(1&๐‘๐‘&๐‘Ž(๐‘+๐‘)@1&๐‘๐‘Ž&๐‘(๐‘+๐‘Ž)@1&๐‘Ž๐‘&๐‘(๐‘Ž+๐‘))| = 0 |โ– 8(1&๐‘๐‘&๐‘Ž(๐‘+๐‘)@1&๐‘๐‘Ž&๐‘(๐‘+๐‘Ž)@1&๐‘Ž๐‘&๐‘(๐‘Ž+๐‘))| = |โ– 8(1&๐‘๐‘&๐‘Ž๐‘+๐‘Ž๐‘@1&๐‘๐‘Ž&๐‘๐‘+๐‘๐‘Ž@1&๐‘Ž๐‘&๐‘๐‘Ž+๐‘๐‘)| C3 โ†’ C3 + C2 = |โ– 8(1&๐‘๐‘&๐‘Ž๐‘+๐‘Ž๐‘+๐‘๐‘@1&๐‘๐‘Ž&๐‘๐‘+๐‘๐‘Ž+๐‘๐‘@1&๐‘Ž๐‘&๐‘๐‘Ž+๐‘๐‘+๐‘๐‘)| Taking (๐‘Ž๐‘+๐‘Ž๐‘+๐‘๐‘) common from C3 = (๐‘Ž๐‘+๐‘Ž๐‘+๐‘๐‘) |โ– 8(๐Ÿ&๐‘๐‘&๐Ÿ@๐Ÿ&๐‘๐‘Ž&๐Ÿ@๐Ÿ&๐‘Ž๐‘&๐Ÿ)| C1 and C3 is same = 0 By Property: if any two row or columns of a determinant are identical then value of determinant is zero

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.