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 Ex 4.4, 2 - Write Minors, Cofactors of determinants - Class 12 - Finding Minors and cofactors

Ex 4.4, 2 - Chapter 4 Class 12 Determinants - Part 2
Ex 4.4, 2 - Chapter 4 Class 12 Determinants - Part 3

 

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Transcript

Ex 4.4, 2 Write Minors and Cofactors of the elements of determinants: (i) |■8(1&0&0@0&1&0@0&0&1)| Minor of a11 = M11 = |■8(1&0&0@0&1&0@0&0&1)| = |■8(1&0@0&1)| = 1(1) – 0 = 1 Minor of a12 = M12 = |■8(1&0&0@0&1&0@0&0&1)| = |■8(0&0@0&1)| = 0 – 0 = 0 Minor of a13 = M13 = |■8(1&0&0@0&1&0@0&0&1)| = |■8(0&1@0&0)| = 0 – 0 = 0 Minor of a21 = M21 = |■8(1&0&0@0&1&0@0&0&1)| = |■8(0&0@0&1)| = 0 – 0 = 0 Minor of a22 = M22 = |■8(1&0&0@0&1&0@0&0&1)| = |■8(1&0@0&1)| = 1 – 0 = 1 Minor of a23 = M23 = |■8(1&0&0@0&1&0@0&0&1)| = |■8(1&0@0&0)| = 0 – 0 = 0 Minor of a31 = M31 = |■8(1&0&0@0&1&0@0&0&1)| = |■8(0&0@1&0)| = 0 – 0 = 0 Minor of a32 = M32 = |■8(1&0&0@0&1&0@0&0&1)| = |■8(1&0@0&0)| = 0 – 0 = 0 Minor of a33 = M33 = |■8(1&0&0@0&1&0@0&0&1)| = |■8(1&0@0&1)| = 1 – 0 = 1 Cofactor of 𝑎_𝑖𝑗= 𝐴_𝑖𝑗 = (−1)^(𝑖+𝑗). 𝑀_𝑖𝑗 Cofactor of a11 = A11 = (–1)1+1 M11= (–1)2 × 1= 1 × 1 = 1 Cofactor of a12 = A12 = (–1)1+2 M12= (–1)3 0 = 0 Cofactor of a13 = A13 = (–1)1+3 M13 = (–1)4 0 = 0 Cofactor of a21 = A21 = (–1)2+1 M21 = (–1)3 0 = 0 Cofactor of a22 = A22 = (–1)2+2 M22 = (–1)4 1 = 1 . 1 = 1 Cofactor of a23 = A23 = (–1)3 + 1 M23 = (–1)4 0 = 0 Cofactor of a31 = A31 = (–1)3 + 1 M31 = (–1)4 0 = 0 Cofactor of a32 = A32 = (–1)3 + 2 M32 = (–1)5 0 = 0 Cofactor of a33 = A33 = (–1)3 + 3 M33 = (–1)6 . 1 = 1 . 1 = 1

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.