Prove that if W is a Subspace of a Finite Dimensional Vector Space Paper

Please complete the exercises in the files with steps

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55. (a) Prove that if W is a subspace of a finite-dimensional vec-
tor space V, then the mapping T:V W defined by
T(v) = projwv is a linear transformation.
(b) What are the range and kernel of the transformation in
part (a)?
3. Use the Gram-Schmidt process to construct an orthogonal basis of the
subspace of V = Cº[0, 1] spanned by f(x) = 1, g(x) = x, and h(x)
where V has the inner product defined by < f, g >= So f (x)g(x)dx.
px