Ex 4.5, 7 - Chapter 4 Class 12 Determinants
Last updated at April 16, 2024 by Teachoo
Find solution of equations- Equations given
Find solution of equations- Equations given
Last updated at April 16, 2024 by Teachoo
Ex 4.5, 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(๐ฅ@๐ฆ)] = [โ 8(4@5)] Hence A = [โ 8(5&2@7&3)], X = [โ 8(๐ฅ@๐ฆ)] & 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 Aโ1 A-1 = 1/(|A|) adj (A) A = [โ 8(5&2@7&3)] adj A = [โ 8(5&2@7&3)] = [โ 8(3&โ2@โ7&5)] Now, A-1 = 1/(|A|) adj A Putting values = 1/1 [โ 8(3&โ2@โ7&5)] = [โ 8(3&โ2@โ7&5)] Now X = A-1 B [โ 8(๐ฅ@๐ฆ)] = [โ 8(3&โ2@โ7&5)] [โ 8(4@5)] [โ 8(๐ฅ@๐ฆ)] = [โ 8(3(4)+(โคถ7โ2)5@โ7(4)+5(5))] [โ 8(๐ฅ@๐ฆ)] = [โ 8(2@โ3)] Hence, x = 2 & y = โ3