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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


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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.