Polynomial Vector - Linear Combination..

[YounGMessiah]

Hey all, I have a problem on one of my labs and my professor hasn't gone over it and I don't have my book lol..

So.. Figured since I gotten great help a couple times on Math, why not ask..

The question is:

If possible, write the polynomial "vector" q(x)=1+x+2x^2 as a linear combination of: p_1(x)=1+2x+3x^2, p_2(x)=1+4x+6x^2, p_3(x)=2-3x-5x^2

Says setup equations by hand, but not sure how the form is..

I'm guessing something along these lines:

a_0 + a_1(1 2 3) + a_2(1 4 6) + a_3(2 -3 -5) = 1+x+2x^2

TIA

Underscore represents subscript

[delta13]

you have to choose a basis set of vectors, in this case polynomials, e.g. {1,x,x^2} and write the polynomials in the problem w.r.t this basis. then you write this representation into a matrix and check whether the kernel of the matrix is trivial. this is a general way to check for linear independence.

ah wait, you want to write q as a linear combination of p1,p2,p3. then you have to do a basis transformation from the canonical basis to basis {p1,p2,p3}. you can look it up on wikipedia.

[YounGMessiah]

This dang talk of basis, spanning and such is so damn hard to grasp lol.. I somewhat understand what you're saying and my professor is discussing what you said.

Argggg, I just haven't had enough practice on this.