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#### bamuelsanks

##### New member

- Apr 2, 2012

- 3

I've been working on a question which is as follows:

For which real values of c will the set $\{1+cx, 1+cx^2, x-x^2\}$ be a basis for $P_2$?

I'm coming up with the answer as no values of c, but am I really wrong?

I've only checked linear independence, because it would imply that it spans $P_2$ (right?)

I figure one would just create the augmented matrix:

$\left( \begin{array}{ccc} 0 & c & 1 \\ 1 & 0 & 1 \\-1 & 1 & 0\end{array} \right)$

And reduce:

$\left( \begin{array}{ccc} 1 & 0 & \frac{1}{c} \\ 0 & 1 & \frac{1}{c} \\ 0 & 0 & 0\end{array} \right)$

Thanks in advance,

SB