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JAMB Mathematics 2022 Question 14

Question 14

Matrices and Determinants

Find the value of P if |−2 1 1; 2 1 P; 1 2 −1| = 23 (rows of the determinant separated by semicolons)

  1. A.1
  2. B.−21/2
  3. C.16/5
  4. D.3
Show the answer and explanation

Answer: C (16/5)

Explanation

Expand along the top row: −2(−1 − 2P) − 1(−2 − P) + 1(4 − 1) = 2 + 4P + 2 + P + 3 = 7 + 5P. Setting 7 + 5P = 23 gives P = 16/5.