Linear algebra

I need the solution for these

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Q.5 (10) Represent the polynomial f(x) = 1 + 2x + 3×2 as a linear combination of the vectors in
the ONB for P2(R).
Q.6 (10) Apply the Gram-Schmidt process to the given subset S of the inner product vector space
V to obtain an ONB for span(S).
V = C4 S = {(1,1,2-1,-1), (2 +31,31, 1-2, 21).(-1 + 71,6+101, 11 – 41, 3+4i)).
where i = -1.
Q.7 (10) Consider a linear transformation T:R? → R’, which satisfies
T
and T
5-01
(a) Find the matrix A of this linear transformation.
(b) Compute its reduced row-echelon form E = rref(A).
(c) Does there exist a vector ERP such that
12
T(?) =
4
?
3
Explain.
Q.8 (10) Show that a basis for R^ cannot have more than n vectors.