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Find the determinant of P

October 13, 2026Mathematics

ScanSolve AI Answer

Answer

-9

3 steps

Find the determinant of P:
Given the matrix $P = \begin{pmatrix} 1 & 3 & 2 \\ 4 & 3 & -1 \\ 3 & 2 & 0 \end{pmatrix}$ .

Calculate the determinant using cofactor expansion along the first row.
$|P| = 1 \begin{vmatrix} 3 & -1 \\ 2 & 0 \end{vmatrix} - 3 \begin{vmatrix} 4 & -1 \\ 3 & 0 \end{vmatrix} + 2 \begin{vmatrix} 4 & 3 \\ 3 & 2 \end{vmatrix}$
Evaluate the $2 \times 2$ determinants.
$|P| = 1((3)(0) - (-1)(2)) - 3((4)(0) - (-1)(3)) + 2((4)(2) - (3)(3))$ $|P| = 1(0 + 2) - 3(0 + 3) + 2(8 - 9)$ $|P| = 1(2) - 3(3) + 2(-1)$
Perform the multiplications and additions/subtractions.
$|P| = 2 - 9 - 2$ $|P| = -7 - 2$ $|P| = -9$
The determinant of P is $-9$ .

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