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Consider the system of equations where a, b, c, d 0,1 Statement 1 The probability that the system of equations has a unique solution, is 3 / 8 . Statement 2 The probability that the system of equations has a solution, is 1 .

Options

  1. AStatement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  2. BStatement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
  3. CStatement 1 is true, Statement 2 is false.
  4. DStatement 1 is false, Statement 2 is true

Correct answer

B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

Step-by-step solution

The number of all possible deteminants of the form Out of which only 10 determinants given by vanish and remaining six determinants have non-zero values. Hence, the required probability = 6 16 = 3 8 Statement 1 is correct. Statement 2 is also correct as the homogeneous equations have always a solution and Statement 2 is not a correct explanation of Statement 1.

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