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JEE Main202125 Jul 2021Morning ShiftMathematicsDeterminantsActual

The values of a and b , for which the system of equations 2 x + 3 y + 6 z = 8 x + 2 y + a z = 5 3 x + 5 y + 9 z = b has no solution, are :

Options

  1. Aa = 3 , b ≠ 13
  2. Ba ≠ 3 , b ≠ 13
  3. Ca ≠ 3 , b = 3
  4. Da = 3 , b = 13

Correct answer

A. a = 3 , b ≠ 13

Step-by-step solution

The given equation is 2 x + 3 y + 6 z = 8 x + 2 y + a z = 5 3 x + 5 y + 9 z = b So, D = 2 3 6 1 2 a 3 5 9 = 2 18 - 5 a - 3 9 - 3 a + 6 5 - 6 = 36 - 10 a - 27 + 9 a + 30 - 36 = 3 - a D z = 2 3 8 1 2 5 3 5   b = 2 2 b - 10 - 3 b - 15 + 8 5 - 6 = 4 b - 20 - 3 b + 15 + 40 - 48 = b - 13 The system of equation has no solution if D = 0   &   D z ≠ 0 So, If a = 3 ,   b ≠ 13 , then the system of equation has no solution.

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