For which values of the constants b and c is the following matrix invertible? (The following is all one matrix)
[ 0 1 b]
[-1 0 c]
[-b -c 0]
I'll suggest some things before one of the wonderful members gives better advice.
You know that invertible matrices must have a non-zero determinant, so maybe calculating that can lead to some conclusions. The columns and rows must also be linearly independent, so I would think about that. Hope that helps some...
well if you're going to reduce row echelon form it, you can always set it up like:
$\displaystyle
\left [\begin{array}{ccc}
0 & 1 & b \\
-1 & 0 & c \\
-b & -c & 0 \end{array} \Bigg|\begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1 \\
\end{array} \right]
$
And reduce that and you can see what values you need to set b and c to be, to make it invertible.
Though you automatically know that b and c cannot both be zero and $\displaystyle b \ne c$ otherwise it'd be not invertible.