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JAMB Mathematics 2000 Question 18

Question 18

Matrices and Determinants

Find the values of t, for which the determinant of the matrix [t − 4, 0, 0; −1, t + 1, 1; 3, 4, t − 2] is zero

  1. A.0, 2, 3
  2. B.−4, 2, 3
  3. C.−4, −2, 3−3
  4. D.4, −2, 3
Show the answer and explanation

Answer: D (4, −2, 3)

Explanation

Expanding along the first row: (t − 4)[(t + 1)(t − 2) − 4] = (t − 4)(t2 − t − 6) = (t − 4)(t − 3)(t + 2). It is zero when t = 4, −2 or 3.