# Find a basis and dimension of the subspace R^n spanned by the following sets

I need a little help with this question: Find a basis and dimension of the subspace R^n spanned by the following set:

{(1,3),(-1,2),(7,6)} (n=2)

I have tried attempting the question by putting the vectors in an augmented matrix and reducing it to row echelon form followed by taking the leading entries as the basis. I got {(1,3),(-1,2)} as my answer for the basis and 2 as the dimension. However, the solution provided {(1,0),(0,1)} as the answer for the basis.

I do not know where I'm going wrong with my answer. I would really appreciate it if I could get a little help on this question.

Thank You! :)

• Hint: is a basis unique? – IdentityMatrix Apr 21 '18 at 14:27

Both answers are correct. The space spanned by those vectors is $\mathbb{R}^2$, and both $\bigl((1,0),(0,1)\bigr)$ and $\bigl((1,3),(-1,2)\bigr)$ are bases of $\mathbb{R}^2$.
• @Jenny It's perhaps the most natural basis of $\mathbb{R}^2$. – José Carlos Santos Apr 21 '18 at 14:30