# Thread: n rows determinant value 6

1. ## n rows determinant value 6

$\begin{vmatrix}
1 &. &. &. & &1 \\
0&1 & & .& . & 1\\
1& & 2& & &1 \\
.& & & 3& & 1\\
.& & & & . & 1\\
1& & & & & n-1
\end{vmatrix}$
=-(n-2)!

is it true

2. Originally Posted by transgalactic
$\begin{vmatrix}
1 &. &. &. & &1 \\
0&1 & & .& . & 1\\
1& & 2& & &1 \\
.& & & 3& & 1\\
.& & & & . & 1\\
1& & & & & n-1
\end{vmatrix}$
=-(n-2)!

is it true
It's not clear what the values that are "dotted" are supposed to be. One? Zero? Regardless, the easiest (i.e. least clever) is to proceed by induction and use partitioned matrix multiplication.

3. dots means that 1 appears n-1 times to the length and to the height

4. from row reduction i got
$\begin{vmatrix}
1 &1 &... & & &1 \\
-1&0 & 0 &...& 0 & 0\\
0& 0 & 1& 0.. & &0 \\
.& 0 &0 & 2& .. & 0\\
.& 0&0 &0 & . & 0\\
0& 0 &.. & & & n-1
\end{vmatrix}$

how to find this determinant

5. Expand on the left column.