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

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  1. Chapter 4 Class 12 Determinants
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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 Now System of equation is x + y + z = 1 2x + 3y + 2z = 2 x + y + 2y = 4 Step 1 Write equation as AX = B 1 1 1 2 3 2 1 1 2 = 1 2 4 Hence A = 1 1 1 2 3 2 1 1 2 , X = & B = 1 2 4 Step 2 Calculate |A| |A| = 1 1 1 2 3 2 1 1 2 = 1 3 2 1 2 1 3 2 1 2 + 1 2 3 1 1 = 1(6 2) 1(4 2) + 1 (2 3)= 1 (4) 1 (2) + 1 ( 1) = 4 2 1 = 1 0 Since |A| 0 Hence system of equation is consistent

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