Topic: Engineering Mathematics
Given P is a matrix = $\begin{pmatrix} 3 & 2 & 1 & 4 \\ 4 & 0 & 3 & 1 \\ 6 & 4 & 2 & 8 \\ 2 & 5 & 1 & 3 \end{pmatrix}$
If det |P| denotes the determinant of matrix P, then which of the following is true:
- A. det P is indeterminate
- B. det P is negative
- C. det |P|=0
- D. None of the above
Answer: C. det |P|=0
Explanation: In matrix P, the third row (6, 4, 2, 8) is exactly twice the first row (3, 2, 1, 4). Since two rows are linearly dependent (proportional), the determinant of the matrix is 0.