Ex 4.5

Chapter 4 Class 12 Determinants
Serial order wise

### Transcript

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(๐ฅ@๐ฆ)] = [โ 8(3@5)] Hence A = [โ 8(5&2@3&2)], X = [โ 8(๐ฅ@๐ฆ)] & B = [โ 8(3@5)] Calculating |A| |A| = |โ 8(5&2@3&2)| = 5(2) โ3(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&โ2@โ3&5)] Now, A-1 = 1/(|A|) adj A A-1 = 1/4 [โ 8(2&โ2@โ3&5)] Thus, X = A-1 B [โ 8(๐ฅ@๐ฆ)] = 1/4 [โ 8(2&โ2@โ3&5)] [โ 8(3@5)] = 1/4 [โ 8(2(3)+(โคถ7โ2)5@โ3(3)+5 (5))] [โ 8(๐ฅ@๐ฆ)] = 1/4 [โ 8(6โ10@โ9+25)] = 1/4 [โ 8(โ4@16)] [โ 8(๐ฅ@๐ฆ)] = [โ 8(โ1@4)] Hence, x = โ1 & y = 4

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.