Prove coordinate vectors are unique for given basis

[csc2iffy]

Homework Statement

Prove that the coordinates of a vector v in a vector space Vn are unique with respect to a given basis B={b1,b2,...,bn}

Homework Equations

The Attempt at a Solution

not sure at all what to do with this

 

[radou]

OK, this is very straightforward. Assume you can represent a vector v as two linear combinations of the basis vectors with different coefficients. After that you only need to use a fundamental property of the basis vectors and that's it.

 

[Rockoz]

Well you want to show that it's unique. A strategy that's good for this kind of proof is to assume the opposite, work with that assumption, and then arrive at something that shows that it must be unique.

To get started:
Well what's the opposite of being unique? How about we assume that a vector can be represented by this basis in two different ways as a linear combination but with different constants. What do you think you can do with this? Think about how you could manipulate this to show that the constants must be the same. You'll need to know properties of a basis to make it work.