Ex 4.5, 1

Transcript

Ex 4.5, 1 (Method 1) Find adjoint of each of the matrices. 1﷮2﷮3﷮4﷯﷯ Let A = 1﷮2﷮3﷮4﷯﷯ adj A = A11﷮A21﷮A12﷮A22﷯﷯ Step1: Calculate minors M11 = 2﷮2﷮3﷮4﷯﷯ = 4 M12 = 2﷮2﷮3﷮4﷯﷯= 3 M21 = 1﷮2﷮3﷮4﷯﷯ = 2 M22 = 1﷮2﷮3﷮4﷯﷯ = 1 Step2: Calculate cofactors A11 = ( – 1)﷮1+1﷯ . M11 = ( – 1)﷮2﷯ 4 = 4 A12 = ( – 1)﷮1+2﷯ . M12 = ( – 1)﷮3﷯ (3) = ( – 1) (3) = –3 A21 = ( – 1)﷮2+1﷯ . M21 = ( – 1)﷮3﷯ 2 = ( – 1) (2) = –2 A22 = ( – 1)﷮2+2﷯ (1) = ( – 1)﷮4﷯ (1) = 1 Step 3: Calculate adjoint adj A = A11﷮A12﷮A21﷮A22﷯﷯ = 4﷮−2﷮−3﷮1﷯﷯ Ex 4.5, 1 (Method 2) Find adjoint of each of the matrices. 1﷮2﷮3﷮4﷯﷯ A = 1﷮2﷮3﷮4﷯﷯ adj A = 1﷮2﷮3﷮4﷯﷯ = 4﷮−2﷮−3﷮1﷯﷯