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Ex 4.5, 6 Examine the consistency of the system of equations. 5x − y + 4z = 5 2x + 3y + 5z = 2 5x − 2y + 6z = −1 The system of equations is 5x − y + 4z = 5 2x + 3y + 5z = 2 5x − 2y + 6z = −1 Writing equation as AX = B [■8(5&−1&4@2&3&5@5&−2&6)] [■8(𝑥@𝑦@𝑧)] = [■8(5@2@−1)] Hence A = [■8(5&−1&4@2&3&5@5&−2&6)], X = [■8(𝑥@𝑦@𝑧)] & B = [■8(5@2@−1)] Calculating |A| |A| = |■8(5&−1&4@2&3&5@5&−2&6)| = 5 |■8(3&5@−2&6)| – 1 (–1) |■8(2&5@5&6)| + 4|■8(2&3@5&−2)| = 5 (18 + 10) + 1(12 – 25) + 4(–4 – 15) = 5 (28) + 1 (–13) + 4(–19) = 140 – 13 – 76 = 51 ≠ 0 Since |A| ≠ 0 The given system of equation is consistent

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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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.