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Properties of Determinant
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Properties of Determinant
Last updated at May 29, 2023 by Teachoo
Question 4 Using the property of determinants and without expanding, prove that: |β 8(1&ππ&π(π+π)@1&ππ&π(π+π)@1&ππ&π(π+π))| = 0 |β 8(1&ππ&π(π+π)@1&ππ&π(π+π)@1&ππ&π(π+π))| = |β 8(1&ππ&ππ+ππ@1&ππ&ππ+ππ@1&ππ&ππ+ππ)| C3 β C3 + C2 = |β 8(1&ππ&ππ+ππ+ππ@1&ππ&ππ+ππ+ππ@1&ππ&ππ+ππ+ππ)| Taking (ππ+ππ+ππ) common from C3 = (ππ+ππ+ππ) |β 8(π&ππ&π@π&ππ&π@π&ππ&π)| 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