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
  2. Serial order wise
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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﷮𝑎﷯ Now System of equation is x + y + z = 1 2x + 3y + 2z = 2 x + y + 2y = 4﷮𝑎﷯ Step 1 Write equation as AX = B 1﷮1﷮1﷮2﷮3﷮2﷮1﷮1﷮2﷯﷯ 𝑥﷮𝑦﷮𝑧﷯﷯ = 1﷮2﷮ 4﷮𝑎﷯﷯﷯ Hence A = 1﷮1﷮1﷮2﷮3﷮2﷮1﷮1﷮2﷯﷯ , X = 𝑥﷮𝑦﷮𝑧﷯﷯ & B = 1﷮2﷮ 4﷮𝑎﷯﷯﷯ 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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