If P = \(\begin{pmatrix}1 & 3 & 2 \\ 4 & 5 & -1 \\ -3 & 2 & 0 \end{pmatrix}\), find the determinant of matrix P.
To find the determinant of the matrix
\(P = \begin{pmatrix} 1 & 3 & 2 \\ 4 & 5 & -1 \\ -3 & 2 & 0 \end{pmatrix}\)
We use the formula:
\(\text{det}(P) = a(ei - fh) - b(di - fg) + c(dh - eg)\)
Substituting the values:
- \(a = 1\), \(b = 3\), \(c = 2\)
- \(d = 4\), \(e = 5\), \(f = -1\)
- \(g = -3\), \(h = 2\), \(i = 0\)
Calculating:
\(ei - fh = 5 \cdot 0 - (-1) \cdot 2 = 2,\)
\(di - fg = 4 \cdot 0 - (-1) \cdot -3 = -3,\)
\(dh - eg = 4 \cdot 2 - 5 \cdot -3 = 8 + 15 = 23.\)
Thus,
\(\text{det}(P) = 1 \cdot 2 - 3 \cdot (-3) + 2 \cdot 23 = 2 + 9 + 46 = 57\)
The determinant of matrix \( P \) is 57
There is an explanation video available below.
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