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Ex 4.6, 6 - Examine consistency 5x - y + 4z = 5, 2x + 3y + 5z

Ex 4.6, 6 - Chapter 4 Class 12 Determinants - Part 2


Transcript

Ex 4.6, 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&[email protected]&3&[email protected]&−2&6)] [■8(𝑥@𝑦@𝑧)] = [■8([email protected]@−1)] Hence A = [■8(5&−1&[email protected]&3&[email protected]&−2&6)], X = [■8(𝑥@𝑦@𝑧)] & B = [■8([email protected]@−1)] Calculating |A| |A| = |■8(5&−1&[email protected]&3&[email protected]&−2&6)| = 5 |■8(3&[email protected]−2&6)| – 1 (–1) |■8(2&[email protected]&6)| + 4|■8(2&[email protected]&−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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.