I have this question, and I'm not really sure how to go about it. Any help would be appreciated:(adsbygoogle = window.adsbygoogle || []).push({});

* Here is the question that is asked. (It is supposed to be a general question, and the question will change for the test. Thus, there may be 4 poly's to work with, or 2... etc.) *

[tex]

P_1(x)=x^2+\alpha

[/tex]

[tex]

P_2(x)=x-\alpha

[/tex]

[tex]

P_3(x)=x^2+x+1

[/tex]

For what values of parameter [tex] \alpha [/tex] form a spanning set for [tex]P_3[/tex].

* This is what I have so far. I'm not sure if I'm going about it right. So this is where I need help :) *

Ok, so I know that a spanning set of [tex]P_3[/tex] must contain at least 3 vectors that are linearly independent.

IF the system is true:

[tex]

\left( \begin{array}{ccc}

P_1(x) & 0 \\

P_2(x) & 0 \\

P_3(x) & 0 \\

\end{array} \right)

[/tex]

THEN the vectors are linearly dependent.

So if we setup the system:

[tex]

\left( \begin{array}{cccc}

1 & 0 & 1 & 0 \\

0 & 1 & 1 & 0 \\

\alpha & -\alpha & 1 & 0

\end{array} \right)

[/tex]

wherever [tex] \alpha [/tex] causes the system to not equal 0 would be when the poly's span [tex] P3 [/tex] right?

if this is right, then how do I show this?

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# For what values of paramater form a spanning set for P3

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