So I have the quadratic form $x^2+3y^2-z^2+6xy-4xz$ and I found the following 3x3 symmetric matrix (I would include working but my formatting isn't very good so just take my word)

$\begin{bmatrix} 1 & 3 & -2 \\ 3 & 3 & 0 \\ -2 & 0 & -1 \end{bmatrix} $

I then have to diagonalise the matrix, and well basically I can't, but if it wasn't diagonalisable then I wouldn't be asked to do it, so I'm just wondering is my answer right?