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Ex 4.5

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Chapter 4 Class 12 Determinants

Serial order wise

Last updated at Feb. 9, 2022 by Teachoo

Ex 4.5, 1 (Method 1) Find adjoint of each of the matrices. [■8(1&[email protected]&4)] A = [■8(1&[email protected]&4)] adj A = [■8(1&[email protected]&4)] = [■8(𝟒&−𝟐@−𝟑&𝟏)] Ex 4.5, 1 (Method 2) Find adjoint of each of the matrices. [■8(1&[email protected]&4)] Let A = [■8(1&[email protected]&4)] adj A =[■8(𝐴11&𝐴[email protected]𝐴12&𝐴22)] Step 1: Calculate minors M11 = |■8(2&[email protected]&4)| M12 = |■8(2&[email protected]&4)| M21 = |■8(1&[email protected]&4)| M22 = |■8(1&[email protected]&4)|Step 2: 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 = [■8(A11&[email protected]&A22)] = [■8(𝟒&−𝟐@−𝟑&𝟏)]