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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&1@2&3&2@1&1&2)] [β– 8(π‘₯@𝑦@𝑧)] = [β– 8(1@2@4/π‘Ž)] Hence, A = [β– 8(1&1&1@2&3&2@1&1&2)] , X =[β– 8(π‘₯@𝑦@𝑧)] & B =[β– 8(1@2@4/π‘Ž)] Calculating |A| |A| = |β– 8(1&1&1@2&3&2@1&1&2)| = 1 |β– 8(3&2@1&2)| –1 |β– 8(2&2@1&2)| +1|β– 8(2&3@1&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

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.