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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise

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 = 4/๐‘Ž Now System of equation is x + y + z = 1 2x + 3y + 2z = 2 x + y + 2y = 4/๐‘Ž Writing equation as AX = B [โ– 8(1&1&1@2&3&2@1&1&2)] [โ– 8(๐‘ฅ@๐‘ฆ@๐‘ง)] = [โ– 8(1@2@4/๐‘Ž)] Hence, A = [โ– 8(1&1&1@2&3&2@1&1&2)] , X =[โ– 8(๐‘ฅ@๐‘ฆ@๐‘ง)] & B =[โ– 8(1@2@4/๐‘Ž)] Calculating |A| |A| = |โ– 8(1&1&1@2&3&2@1&1&2)| = 1 |โ– 8(3&2@1&2)| โ€“1 |โ– 8(2&2@1&2)| +1|โ– 8(2&3@1&1)| = 1(6 โ€“ 2) โ€“ 1(4 โ€“ 2) + 1 (2 โ€“ 3) = 4 โ€“ 2 โ€“ 1 = 1 โ‰  0 Since |A| โ‰  0 Hence system of equation is consistent

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.