# Interesting matrices

Algebra Level 3

If $$A=(a_{ij})$$ is a $$3\times 3$$ matrix such that $$a_{ij}=i$$ for $$i\leq j$$ and $$a_{ij}=-a_{ji}$$ for $$i>j,$$ and $A=\left(\begin{array}{ccc}y-x&1& x-z\\-1& y-z&2\\x-y&-2& x+z \end{array}\right),$ what is the value of $$x+y+z?$$

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