How to find basis vectors for a+ ax^2+bx^4?

DhineshKumar
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I want to find basis for a+ax^2+bx^4 belong to p4.
I am getting the following result is it right?
=>a(1+x^2) + b(x^4)
=> basis ={1+x^2, x^4}

Is that right ? Please help me any help is appreciated.
 
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Since you only have two terms (a,b) it makes sense to have a basis with two vectors. This function will be in the span of those bases for any choice of a and b.
In the standard polynomial basis [1, x, x^2, x^3, x^4,x^5 ... ], this would be [ a, 0, a, 0, b,0,...].
 
Thank you so much.
 
yes
 

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