# Null Space and Linear Independance

If the $N(A)$ has more than just the $\vec{0}$, does that mean that the $C(A)$ is linearly dependant?

Moreover, I just started with Linear Algebra a week ago, so if there is something wrong about my notation of the null space, column vectors etc. Tell me please!

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I am guessing that $N(A)$ is the null space, what is $C(A)$, the columns? –  copper.hat Oct 10 '12 at 19:57
Column vectors of Matrix A. –  JohnPhteven Oct 10 '12 at 19:58

Assuming that $N,C$ refer to the null space and columns respectively, then yes.
If $Ax = 0$, with $x \neq 0$, then this is equivalent to $\sum x_i a_i = 0$, with at least one $x_i \neq 0$, where $a_i$ is the $i$th column of $A$.
Hence the columns of $A$ are linearly dependent iff the null space of $A$ contains a non-zero vector.