Hi, I'm having trouble finding the right values...

Consider the following system I have:

2x - y + z = x

0x + 2y +0z = y

x + 3y +2z = z

So we see from our second equation that 2y=y, thus y=0, thats fine so far

However, I now find z = -x

so this gives us an eigenvector:

1

0

-1

Can someone show me how I get the 1st and 3rd entry for this vector? Because from what i know i thought the 1st entry would also be -1?

A clear explanation would be good thanks