I have matrix:
$ A = \begin{bmatrix} 1 & 2 & 3 & 4 \\ 2 & 3 & 3 & 3 \\ 0 & 1 & 2 & 3 \\ 0 & 0 & 1 & 2 \end{bmatrix} $
And I want to calculate $\det{A}$, so I have written:
$ \begin{array}{|cccc|ccc} 1 & 2 & 3 & 4 & 1 & 2 & 3 \\ 2 & 3 & 3 & 3 & 2 & 3 & 3 \\ 0 & 1 & 2 & 3 & 0 & 1 & 2 \\ 0 & 0 & 1 & 2 & 0 & 0 & 1 \end{array} $
From this I get that:
$ \det{A} = (1 \cdot 3 \cdot 2 \cdot 2 + 2 \cdot 3 \cdot 3 \cdot 0 + 3 \cdot 3 \cdot 0 \cdot 0 + 4 \cdot 2 \cdot 1 \cdot 1) - (3 \cdot 3 \cdot 0 \cdot 2 + 2 \cdot 2 \cdot 3 \cdot 1 + 1 \cdot 3 \cdot 2 \cdot 0 + 4 \cdot 3 \cdot 1 \cdot 0) = (12 + 0 + 0 + 8) - (0 + 12 + 0 + 0) = 8 $
But WolframAlpha is saying that it is equal 0. So my question is where am I wrong?