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anonymous
 5 years ago
Why is the set {1, x, x^2} a basis for P_2 when a+bx+cx^2 = a(1)+b(x)+c(x^2)?
I understand that the this set spans P_2, but how do we know it's linearly independent?
anonymous
 5 years ago
Why is the set {1, x, x^2} a basis for P_2 when a+bx+cx^2 = a(1)+b(x)+c(x^2)? I understand that the this set spans P_2, but how do we know it's linearly independent?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Because no linear combinations of any two of those vectors will yield any of the others.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So, 1, x, and x^2 are all vectors, and k(1)+k(x)=x^2 is not consistent? Same thing with combinations of vectors in the set? I have trouble getting over the fact the something is a vector when it's not expressed in the form (a,b,c) or whatever.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0other vectors in the set*

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The graph of k(1)+k(x) will never equal the graph of x^2. Therefore they are linearly independent.
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