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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 ∆ = |■8(𝑥+𝑦&𝑦" + z" &𝑧+𝑥@𝑧&𝑥&𝑦@1&1&1)| = 0 |■8(𝑥+𝑦&𝑦" + z" &𝑧+𝑥@𝑧&𝑥&𝑦@1&1&1)| Applying R1 → R1 + R2 = |■8(𝑥+𝑦+𝑧&𝑥+𝑦+𝑧&𝑥+𝑦+𝑧@z&𝑥&𝑦@1&1&1)| Taking (x + y + z) common from R1 = (x + y + z) |■8(1&1&1@𝑧&𝑥&𝑦@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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.