# Simple basis question

$\begin{pmatrix} 0&1 \\0 & 0 \end{pmatrix}$

Find the basis of this matrix. The answer is $\begin{pmatrix}1\\0\end{pmatrix}$ I keep getting$\begin{pmatrix}0\\1\end{pmatrix}$

Can anyone help me with the steps. I cant remember how to do this properly.

-
How are you arriving at $\begin{pmatrix}0\\1\end{pmatrix}$? –  amWhy Apr 15 '13 at 2:40
FYI: Matrices do not have bases, vector spaces have bases but a matrix is not a vector space. My guess is that you meant to say you wanted a basis for the column space of that matrix. –  Jim Apr 15 '13 at 2:46
x1 = 0 x2=1 thats how and i am really wrong. Also, jim you are correct. I would appreciate if anyone can show me the steps. –  user1730308 Apr 15 '13 at 2:59
To find a basis, find a set that spans the space and prove that it is linearly independent –  Justin Apr 15 '13 at 5:21

## 1 Answer

Hint: (assuming the OP wants a basis for column space) First column is the zero vector. There are only two columns.

-
I believe someone downvoted this as it is not clear. Can you add updates to better explain? Regards –  Amzoti Apr 15 '13 at 3:01
The hint is good if the OP meant the column space (as he says he did), yet the question is so sloppy that someone perhaps thought the answerer was guessing. I'm upvotingthis answer to balance...and because it is suposed to be a good hint for anyone really understanding what the OP asks. –  DonAntonio Apr 15 '13 at 3:38