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Ex 4.5, 2 - Find adjoint of matrix - Chapter 4 Determinants - Ex 4.5

Ex 4.5, 2 - Chapter 4 Class 12 Determinants - Part 2
Ex 4.5, 2 - Chapter 4 Class 12 Determinants - Part 3

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Ex 4.5, 2 Find adjoint of each of the matrices. 1 1 2 2 3 5 2 0 1 Let A = 1 1 2 2 3 5 2 0 1 adj A = A11 A21 A31 A12 A22 A32 A13 A23 A33 Step 1: Cacluating minors M11 = 3 5 0 1 = 3(1) 0(5) = 3 0 = 3 M12 = 2 5 2 1 = 2 ( 10) = 2 + 10 = 12 M13 = 2 3 2 0 = 0 ( 6) = 0 + 6 = 6 M21 = 1 2 0 1 = 1 (0) = 1 + 0 = 1 M22 = 1 2 2 1 = 1 (-2)2 = 1 + 4 = 5 M23 = 1 1 2 0 = 0 ( 2) ( 1) = 0 (2) = 2 M31 = 1 2 3 5 = 5 ( 1) 6 = 5 6 = 11 M32 = 1 2 2 5 = 5 4 = 1 M33 = 1 1 2 3 = 3 ( 2) = 3 + 2 = 5 Step 2: Calculating adjoint A11 = ( 1) 1+1 . M11 = ( 1)2 . 3 = 3 A12 = ( 1) 1+2 . M12 = ( 1) 3 . (12) = 1 (12) = 12 A13 = ( 1) 1+3 . M13 = ( 1) 4 . ( 6) = 1(6) = 6 A21 = ( 1) 2+1 . M21 = ( 1) 3 . (-1) = -1(-1) = 1 A22 = ( 1) 2+2 . M22 = ( 1) 4 . (5)= 1(5) = 5 A23 = ( 1) 2+3 . M23 = ( 1) 5 . ( 2) = 1 ( 2) = 2 A31 = ( 1) 3+1 . M31 = ( 1) 4 . ( 11) = 1 ( 11) = 11 A32 = ( 1) 3+2 . M32 = ( 1) 5 . (1) = ( 1) (1) = 1 A33 = ( 1) 3+3 . M33 = ( 1)6 . ( 5) = 1 (5) = 5 Step 3: Calculating adjoint Hence, adj A = A11 A21 A31 A12 A22 A32 A13 A23 A33 = 3 1 11 12 5 1 6 2 5

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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.