Exercises 15 and 16 provide a proof of Theorem 15. Fill in a justification for each step.
15. Given v in V. there exist scalars x1, …., xn. such that
v = x1b1 + x2b2 + … + xnbn
because (a) ______. Apply the coordinate mapping deter-mined by the basis C. and obtain
[v]C = x1[b1]C + x2[b2]C + … + xn[bn]C
because (b) ______. This equation may be written in the form
[v]C = [[b1]C [b2]C … [bn]C]
by the definition of (c) ______.This shows that the matrix
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