Q:

Confused about the null space of a matrix

Hi I'm trying to find the null space of a matrix. 
I've got an answer I'm a bit confused by.  Is that right?  Would this just mean the zero vector is the only solution? 

A:

Yes, you are correct. 
I double-checked with Wolfram Alpha: https://www.wolframalpha.com/input/?i=null+space+of+%7B%7B1,-1%7D,%7B2,2%7D,%7B5,4%7D%7D
The null space of a matrix $A$, is the set of vectors $x$ such that $Ax=0$. Since you found that the only possibility is $x=0$, so the null space is $\{0\}$.

