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1. The problem statement, all variables and given/known data

Given a vector space V and its basis B = {v_{1}, v_{2}, ..., v_{n}}, I was asked to prove that:

a group of vectors {u_{1},...,u_{k}} in V is linearlydependentif and only if {[u_{1}]_{B},...[u_{k}]_{B}} is linearlydependent.

2. Relevant equations

3. The attempt at a solution

I proved that a group of vectors {u_{1},...,u_{k}} in V is linearlyindependentif and only if {[u_{1}]_{B},...[u_{k}]_{B}} is linearlyindependent. Following the principles of logic, that would be the same as proving dependence, right?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: {u1, ,uk} is linearly dependent iff {[u1]_B, [uk]B} is.

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