Question 23
Matrices and DeterminantsThe determinant of matrix
( x 1 0 )
( 1−x 2 3 )
( 1 1+x 4 )
in terms of x is.
- A.−3x2 − 17
- B.−3x2 + 9x − 1
- C.3x2 + 17
- D.3x2 − 9x + 5
Show the answer and explanation
Answer: B (−3x2 + 9x − 1)
Explanation
Expand along the first row: x[2(4) − 3(1 + x)] − 1[4(1 − x) − 3] = x(5 − 3x) − (1 − 4x) = −3x² + 9x − 1.