# How to find the determinant this unknown sized matrix? [closed]

I've got a matrix $A$ with a size of $(n \times n)$, that can be described like this:

$$A=\begin{bmatrix} 1 & 2 & 3 & \cdots & n \\ -1 & 0 & 3 & \cdots & n \\ -1 & -2 & 0 & \cdots & n \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ -1 & -2 & -3 & \cdots & 0 \\ \end{bmatrix}$$

How would I go about and find the determinant of this matrix (I thought about describing it as a sum but I don't know how to create an equation for any element $a_(ij_)$)?

## closed as off-topic by Lord Shark the Unknown, Leucippus, Claude Leibovici, user91500, ShaileshSep 15 '17 at 9:29

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• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Lord Shark the Unknown, Leucippus, Claude Leibovici, user91500, Shailesh
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Hint: try adding the first row to each of the other rows. That doesn't change the determinant and gives you an upper-triangular matrix.

• "Upper-triangular matrix" is something everyone needs to know about, really makes things simpler. Thanks a lot! – Avamander Sep 14 '17 at 21:23