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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise

Transcript

Ex 4.6, 7 Solve system of linear equations, using matrix method. 5x+ 2y = 4 7x + 3y = 5 The system of equations is 5x + 2y = 4 7x + 3y = 5 Writing equation as AX = B [โ– 8(5&2@7&3)] [โ– 8(๐‘ฅ@๐‘ฆ)] = [โ– 8(4@5)] Hence A = [โ– 8(5&2@7&3)], X = [โ– 8(๐‘ฅ@๐‘ฆ)] & B = [โ– 8(4@5)] Calculating |A| |A| = |โ– 8(5&2@7&3)| = 5(3) โ€“ 7(2) = 15 โ€“ 14 = 1 โ‰  0 Since |A|โ‰  0, System of equations is consistent & has a unique solution Now, AX = B Solution is X = A-1 B Calculating Aโˆ’1 A-1 = 1/(|A|) adj (A) A = [โ– 8(5&2@7&3)] adj A = [โ– 8(5&2@7&3)] = [โ– 8(3&โˆ’2@โˆ’7&5)] Now, A-1 = 1/(|A|) adj A Putting values = 1/1 [โ– 8(3&โˆ’2@โˆ’7&5)] = [โ– 8(3&โˆ’2@โˆ’7&5)] Now X = A-1 B [โ– 8(๐‘ฅ@๐‘ฆ)] = [โ– 8(3&โˆ’2@โˆ’7&5)] [โ– 8(4@5)] [โ– 8(๐‘ฅ@๐‘ฆ)] = [โ– 8(3(4)+(โคถ7โˆ’2)5@โˆ’7(4)+5(5))] [โ– 8(๐‘ฅ@๐‘ฆ)] = [โ– 8(2@โˆ’3)] Hence, x = 2 & y = โ€“3

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.