Question: 7. (6 points) Let B = {by, bs, ..., b, } is a basis for the vector space V. Prove the Unique Representation Theorem, i.e.

7. (6 points) Let B = {by, bs, ..., b, } is a basis for the vector space V. Prove the Unique Representation Theorem, i.e. every vector x of V has a unique set of coordinates. 8. (6 points) Show that if v,, v, 73 are linearly independent, then the vectors Wi = v1+v,, W, = 1, +V3, W3 = v,+V5 are also linearly independent

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