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Ex 4.6, 3 - Examine consistency x + 3y = 5, 2x + 6y = 8 - Ex 4.6

Ex 4.6, 3 - Chapter 4 Class 12 Determinants - Part 2
Ex 4.6, 3 - Chapter 4 Class 12 Determinants - Part 3

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Transcript

Ex 4.6, 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 [■8(1&[email protected]&6)] [■8(𝑥@𝑦)] = [■8([email protected])] Hence A = [■8(1&[email protected]&6)] , X = [■8(𝑥@𝑦)] & B = [■8([email protected])] Calculating |A| |A| = |■8(1&[email protected]&6)| = 1(6) – 2(3) = 6 – 6 = 0 Since |A| = 0, we will calculate (adj A) B A = [■8(1&[email protected]&6)] adj (A) = [■8(1&[email protected]&6)] = [■8(6&−[email protected]−2&1)] Now, (adj A)(B) = [■8(6&−[email protected]−2&1)] [■8([email protected])] = [■8(6(5)+(⤶7−3)[email protected]−2(5)+1(8))] = [■8(30−[email protected]−10+8)] = [■8([email protected]−2)] ≠ O Since adj A (B) ≠ O & |A| = 0, , There exists no solution, Hence, the given system of equation is inconsistent

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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.