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(Solved): (b) Consider the set P_(2) of all polynomials of degree 2 and the set S={p_(2),p_(2),p_(3)} where p_ ...
(b) Consider the set P_(2) of all polynomials of degree 2 and the set S={p_(2),p_(2),p_(3)}
where p_(1)=1+x,p_(2)=1+x^(2),p_(3)=x+x^(2). Is the set S a basis for P_(2) ? If so, find the
coordinate vector of the polynomial p(x)=2-x+x^(2) relative to the basis S.