For which values of the constantsbandcis the following matrix invertible? (The following is all one matrix)

[ 0 1b]

[-1 0c]

[-b-c0]

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- Sep 17th 2009, 12:15 PMnoles2188Invertible Matrix
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] - Sep 17th 2009, 12:26 PMKrizalid
it's a very straightforward problem, you only need to compute its determinant and set it different from zero.

- Sep 17th 2009, 12:28 PMJameson
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... - Sep 17th 2009, 12:48 PMnoles2188
well the thing is, we haven't learned how to do 3x3 determinants yet. I know how to do it, but we've just been trying to get reduced row echelon form to check invertibility. Any other suggestions?

- Sep 17th 2009, 04:25 PMJameson
- Sep 17th 2009, 06:05 PMseld
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.