Question

K = [ 14 -13 0 3 8 -1 -10 -2 5 ] find the determinant of K

Answer 1

I suppose K is the matrix

`K = \begin{bmatrix}14 & -13 & 0 \\ 3 & 8 & -1 \\ -10 & -2 & 5\end{bmatrix}`

To compute det(K), you can use a simple cofactor expansion along the first row:

`\det(K) = 14*\det\begin{bmatrix}8 & -1 \\-2 & 5\end{bmatrix} - (-13)*\det\begin{bmatrix}3 & -1 \\ -10 & 5\end{bmatrix} + 0*\det\begin{bmatrix}3 & 8 \\ -10 & -2\end{bmatrix} \\\\ \det(K) = 14*(8*5-(-1)*(-2)) + 13*(3*5-(-1)*(-10)) + 0 \\\\ \det(K) = 14*38 + 13*5 = \boxed{597}`