Question

Let W⊂ C1 be the subspace spanned by the two polynomials x1(t) = 1 and x2(t)...

Let W⊂ C1 be the subspace spanned by the two polynomials x1(t) = 1 and x2(t) =t^2. For the given function y(t)=1−t^2 decide whether or not y(t) is an element of W. Furthermore, if y(t)∈W, determine whether the set {y(t), x2(t)} is a spanning set for W.

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