Example 10 Find minors and cofactors of the elements a11, a21 in the determinant ∆ = |■8(a11&a12&a13@a21&a22&a23@a31&a32&a33)| Minor of a11 = M11 = |■8(a11&a12&a13@a21&a22&a23@a31&a32&a33)| = |■8(a22&a23@a32&a33)| = a22 a33 – a23 a32 Minor of a21 = M21 = |■8(a11&a12&a13@a21&a22&a23@a31&a32&a33)| = |■8(a12&a13@a32&a33)| = a12 a33 – a32 a13 Cofactor of a11 = A11 = ( – 1)1+1 . M11 = ( –1)2 . (a22 a33 – a32 a23) = a22 a33 – a32 a23 Cofactor of a21 = A21 = ( – 1)2+1 . M21= ( – 1)3 . (a12 a33 – a32 a13) = ( – 1) . (a12 a33 – a32 a13) = a32 a13 – a12 a33

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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.

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