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Chapter 4 Class 12 Determinants

Serial order wise

Last updated at Jan. 23, 2020 by Teachoo

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 [β 8(5&2@7&3)] [β 8(π₯@π¦)] = [β 8(4@5)] Hence A = [β 8(5&2@7&3)], X = [β 8(π₯@π¦)] & B = [β 8(4@5)] Calculating |A| |A| = |β 8(5&2@7&3)| = 5(3) β 7(2) = 15 β 14 = 1 β 0 Since |A|β 0, System of equations is consistent & has a unique solution Now, AX = B Solution is X = A-1 B Calculating Aβ1 A-1 = 1/(|A|) adj (A) A = [β 8(5&2@7&3)] adj A = [β 8(5&2@7&3)] = [β 8(3&β2@β7&5)] Now, A-1 = 1/(|A|) adj A Putting values = 1/1 [β 8(3&β2@β7&5)] = [β 8(3&β2@β7&5)] Now X = A-1 B [β 8(π₯@π¦)] = [β 8(3&β2@β7&5)] [β 8(4@5)] [β 8(π₯@π¦)] = [β 8(3(4)+(β€Ά7β2)5@β7(4)+5(5))] [β 8(π₯@π¦)] = [β 8(2@β3)] Hence, x = 2 & y = β3