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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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Ex 4.5, 3 Examine the consistency of the system of equations. x + 3y = 5 2x + 6y = 8 x + 3y = 5 2x + 6y = 8 Writing equation as AX = B [โ– 8(1&3@2&6)] [โ– 8(๐‘ฅ@๐‘ฆ)] = [โ– 8(5@8)] Hence A = [โ– 8(1&3@2&6)] , X = [โ– 8(๐‘ฅ@๐‘ฆ)] & B = [โ– 8(5@8)] Calculating |A| |A| = |โ– 8(1&3@2&6)| = 1(6) โ€“ 2(3) = 6 โ€“ 6 = 0 Since |A| = 0, we will calculate (adj A) B A = [โ– 8(1&3@2&6)] adj (A) = [โ– 8(1&3@2&6)] = [โ– 8(6&โˆ’3@โˆ’2&1)] Now, (adj A)(B) = [โ– 8(6&โˆ’3@โˆ’2&1)] [โ– 8(5@8)] = [โ– 8(6(5)+(โคถ7โˆ’3)8@โˆ’2(5)+1(8))] = [โ– 8(30โˆ’24@โˆ’10+8)] = [โ– 8(6@โˆ’2)] โ‰  O Since adj A (B) โ‰  O & |A| = 0, , There exists no solution, Hence, the given system of equation is inconsistent

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.