# Ex 4.5, 10 - Chapter 4 Class 12 Determinants

Last updated at April 16, 2024 by Teachoo

Chapter 4 Class 12 Determinants

Serial order wise

Last updated at April 16, 2024 by Teachoo

Ex 4.5, 10 Solve system of linear equations, using matrix method. 5x + 2y = 3 3x + 2y = 5 The system of equation is 5x + 2y = 3 3x + 2y = 5 Writing above equation as AX = B [โ 8(5&2@3&2)] [โ 8(๐ฅ@๐ฆ)] = [โ 8(3@5)] Hence A = [โ 8(5&2@3&2)], X = [โ 8(๐ฅ@๐ฆ)] & B = [โ 8(3@5)] Calculating |A| |A| = |โ 8(5&2@3&2)| = 5(2) โ3(2) = 10 โ 6 = 4 Since |A| โ 0 The System of equation is consistent & has a unique solution Now, AX = B X = A-1 B Calculating A-1 A-1 = 1/(|A|) adj (A) A =[โ 8(5&2@3&2)] adj A = [โ 8(2&โ2@โ3&5)] Now, A-1 = 1/(|A|) adj A A-1 = 1/4 [โ 8(2&โ2@โ3&5)] Thus, X = A-1 B [โ 8(๐ฅ@๐ฆ)] = 1/4 [โ 8(2&โ2@โ3&5)] [โ 8(3@5)] = 1/4 [โ 8(2(3)+(โคถ7โ2)5@โ3(3)+5 (5))] [โ 8(๐ฅ@๐ฆ)] = 1/4 [โ 8(6โ10@โ9+25)] = 1/4 [โ 8(โ4@16)] [โ 8(๐ฅ@๐ฆ)] = [โ 8(โ1@4)] Hence, x = โ1 & y = 4