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WAEC Further Mathematics 2023 Question 24

Question 24

Matrices and Determinants

Given that P = (x 4 / 3 7), Q = (x 3 / 1 2x) and the determinant of Q is three more than that of P, find the values of x. (Matrices written row by row; / separates the rows.)

  1. A.−2, −3/2
  2. B.−2, 3/2
  3. C.2, −3/2
  4. D.2, 3/2
Show the answer and explanation

Answer: D (2, 3/2)

Explanation

|P| = 7x − 12 and |Q| = 2x² − 3. 2x² − 3 = 7x − 9 gives 2x² − 7x + 6 = 0, (2x − 3)(x − 2) = 0, so x = 2 or 3/2.