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Example 12 - Without expanding, prove that determinant = 0

Example 12 - Chapter 4 Class 12 Determinants - Part 2


Transcript

Example 12 Without expanding, prove that βˆ† = |β– 8(π‘₯+𝑦&𝑦" + z" &𝑧+π‘₯@𝑧&π‘₯&𝑦@1&1&1)| = 0 |β– 8(π‘₯+𝑦&𝑦" + z" &𝑧+π‘₯@𝑧&π‘₯&𝑦@1&1&1)| Applying R1 β†’ R1 + R2 = |β– 8(π‘₯+𝑦+𝑧&π‘₯+𝑦+𝑧&π‘₯+𝑦+𝑧@z&π‘₯&𝑦@1&1&1)| Taking (x + y + z) common from R1 = (x + y + z) |β– 8(1&1&1@𝑧&π‘₯&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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.