Question: Let V = R[x]3, W = R[x]6 be the vector spaces consisting of zero and polynomials in x of degree 3 and degree 6

Let V = R[x]3, W = R[x]6 be the vector spaces consisting

Let V = R[x]3, W = R[x]6 be the vector spaces consisting of zero and polynomials in x of degree 3 and degree 6 respectively. This question concerns the map a: V W which sends a polynomial f(x) in V to f(x) in W. Show that a is linear as a map V W. Find the nullity v(a) and the rank p(a). Let U = Image(a) CW and find a subspace Z C W such that W = U Z. Justify your answers.

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