I know that I can find the determinant by working my way from 4x4 to 3x3 to 2x2 determinant. However that is long.
Which other method can I use?
\begin{bmatrix} 2 & 1 & 0 & 6 \\ 2 & 5 & 3 & 0 \\ 1 & 6 & 0 &-2 \\ 0 &-2 & 5 & -1 \end{bmatrix}
2026-04-25 22:47:31.1777157251
Finding the determinant of a 4x4 matrix quickly
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Substract twice the third row both from the second and the first rows to get:
$$\begin{pmatrix}0&-11&0&10\\0&-7&3&4\\1&6&0&-2\\0&-2&5&-1\end{pmatrix}$$
Develop by the first column and get:
$$\det\begin{pmatrix}-11&0&10\\-7&3&4\\-2&5&-1\end{pmatrix}=33+0-350+220-0+60=-37$$