Question

determine o determinante da seguinte matriz [x 2 1]
[3 -1 x]
[0 2 1]​

Answer 1

$\left|\begin{array}{ccc}x&2&1\\3&-1&x\\0&2&1\end{array}\right|~=\\\\\\=~(~x.(-1).1~+~3.2.1~+~0.2.x~)~-~(~1.(-1).0~+~x.2.x~+~1.2.3~)\\\\\\=~(~-x~+~6~+~0~)~-~(~0~+~2x^2~+~6~)\\\\\\=~(~-x~+~6~)~-~(~2x^2~+~6~)\\\\\\=~-x+6-2x^2-6\\\\\\=~\boxed{-2x^2-x}$