Question 7 - Two rows or columns same - Chapter 4 Class 12 Determinants

Last updated at August 17, 2026 by

Example 12 - Without expanding, prove that determinant = 0

Example 12 - Chapter 4 Class 12 Determinants - Part 2

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Question 7 Without expanding, prove that โˆ† = |โ– 8(๐‘ฅ+๐‘ฆ&๐‘ฆ" + z" &๐‘ง+๐‘ฅ@๐‘ง&๐‘ฅ&๐‘ฆ@1&1&1)| = 0 |โ– 8(๐‘ฅ+๐‘ฆ&๐‘ฆ" + z" &๐‘ง+๐‘ฅ@๐‘ง&๐‘ฅ&๐‘ฆ@1&1&1)| Applying R1 โ†’ R1 + R2 = |โ– 8(๐‘ฅ+๐‘ฆ+๐‘ง&๐‘ฅ+๐‘ฆ+๐‘ง&๐‘ฅ+๐‘ฆ+๐‘ง@z&๐‘ฅ&๐‘ฆ@1&1&1)| Taking (x + y + z) common from R1 = (x + y + z) |โ– 8(1&1&1@๐‘ง&๐‘ฅ&๐‘ฆ@1&1&1)| R1 and R3 are identical = 0 By Property: if any two row or columns of a determinant are identical then value of determinant is zero

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