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## Homework Statement

For which a [tex]\in[/tex] C is the 3x3 matrix:

[tex]\[\left[ \begin{matrix}

a & 2 & 0 \\

0 & -1 & 2 \\

1 & 0 & a \\

\end{matrix} \right]\]

[/tex]

nonsingular ?

## Homework Equations

Ax = 0

## The Attempt at a Solution

Well, the problem is that I think I know what to do, but I can't remember how it's done :S

If Ax = 0, then it's nonsingular, so that's all I have to show.

And then I multiply the matrix with x ([x1, x2, x3]) I just get the same matrix as I have above, but with zeros in the fourth column.

So if I put in on REF I get that x1 = -a, x2 = a

^{2}/2.

And then what ? In my head in seems so easy, but I just can't figure it out :S

What is the a's that's satisfy that the matrix is nonsingular ?

If I use RREF on AB = BA = I, I get that a [tex]\neq[/tex] (+-)2. But I can only do that if I have assumed that the matrix, A, is nonsingular, which I have not shown yet.

So, what to do ? :)

Regards