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Ex 4.6, 4 - Examine consistency x + y + z = 1, 2x + 3y - Ex 4.6

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

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Transcript

Ex 4.6, 4 Examine the consistency of the system of equations. x + y + z = 1 2x + 3y + 2z = 2 ax + ay + 2az = 4 Simplifying 3rd equation ax + ay + 2az = 4 a(x + y + 2z) = 4 x + y + 2z = 4/π‘Ž Now System of equation is x + y + z = 1 2x + 3y + 2z = 2 x + y + 2y = 4/π‘Ž Writing equation as AX = B [β– 8(1&1&[email protected]&3&[email protected]&1&2)] [β– 8(π‘₯@𝑦@𝑧)] = [β– 8([email protected]@4/π‘Ž)] Hence, A = [β– 8(1&1&[email protected]&3&[email protected]&1&2)] , X =[β– 8(π‘₯@𝑦@𝑧)] & B =[β– 8([email protected]@4/π‘Ž)] Calculating |A| |A| = |β– 8(1&1&[email protected]&3&[email protected]&1&2)| = 1 |β– 8(3&[email protected]&2)| –1 |β– 8(2&[email protected]&2)| +1|β– 8(2&[email protected]&1)| = 1(6 – 2) – 1(4 – 2) + 1 (2 – 3) = 4 – 2 – 1 = 1 β‰  0 Since |A| β‰  0 Hence 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.