Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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!

share|cite|improve this question
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
up vote 3 down vote accepted

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.

share|cite|improve this answer
Thank you. If I may ask, and this will probably be a stupid question, why does the zero have a sort of comma in it? Is that the notation for the zero-vector? – JohnPhteven Oct 10 '12 at 20:02
@ZafarS no it happens to me too sometimes, it is not the notation,it is an illusion, you have to adjust the zoom of the screen to see properly what it was written. – clark Oct 10 '12 at 20:06
Ok, and a final small question (I don't think it is worth asking seperately) is this statement correct: Nullity (A) = # of free variables in rref(A)? – JohnPhteven Oct 10 '12 at 20:07
I presume rref is reduced row echelon form. The answer is yes. – copper.hat Oct 10 '12 at 20:21

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.