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Homework Statement
Let A be an m x n matrix with m<n. Prove that the columns of A are linearly dependent.
Homework Equations
Its obvious that for the columns to be linearly dependent they must form a determinate that is equal to 0, or if one of the column vectors can be represented by a linear combination of the other vectors.
The Attempt at a Solution
It seems like there has to be more shown to prove this statement, however this is what I have right now:
Let A be an m x n matrix, and let m < n.
Then the set of n column vectors of A are in Rm and must be linearly dependent.
Is this it? or do I need to state a theorem in here somewhere?