Show that the representation v c 1 a (1) c n a (n) of any given vector in an n dimensional vector space V in terms of a given basis a (1) , , a (n) for V is unique Take two representations and consider the difference

Question: Show that the representation v = c 1 a (1) + . . . + c n a (n) of any given vector in an

Show that the representation v = c₁a₍₁₎ + . . . + c_na_(n) of any given vector in an n-dimensional vector space V in terms of a given basis a₍₁₎, . . ., a_(n) for V is unique. Take two representations and consider the difference.

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