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JAMB Mathematics 1998 Question 24

Question 24

Matrices and Determinants

Let I = (1 0 / 0 1), P = (2 3 / 4 5), Q = (u 4+u / −2v v) be 2 × 2 matrices such that PQ = I. Find (u, v)
(Rows are separated by /.)

  1. A.(−5/2, −1)
  2. B.(−5/2, 3/2)
  3. C.(−5/6, 1)
  4. D.(5/2, 2/3)
Show the answer and explanation

Answer: A ((−5/2, −1))

Explanation

From PQ = I: 2u − 6v = 1 and 4u − 10v = 0. The second gives u = 5v/2; substituting, −v = 1, so v = −1 and u = −5/2.