Question 22
Matrices and DeterminantsUse the matrices below to answer questions 22 and 23.
P = [x 3 0; 2 y 3; 4 2 z] (rows: x, 3, 0 / 2, y, 3 / 4, 2, z)
Q = [x 2 4; 3 y 2; 0 3 z] (rows: x, 2, 4 / 3, y, 2 / 0, 3, z)
When PT is the transpose of P, calculate |PT| when x = 0, y = 1 and z = 2
- A.48
- B.24
- C.−24
- D.−48
Show the answer and explanation
Answer: B (24)
Explanation
A matrix and its transpose have the same determinant. With x = 0, y = 1, z = 2: |P| = 0(2 − 6) − 3(4 − 12) + 0 = 24.