# Basis R 2

Find the basis of the vector space (1,2)^T; (-1,1)^T

When I solve the matrix, I obtain x1=0 and x2=0

x=(0,0)^T.

Can a basis be two 0 column vectors? Thanks for the help.

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No, a basis cannot be two 0 column vectors.
What matrix are you talking about? Are you trying to solve (1,2)x1 + (-1,1)x2 = 0? If so, what does this tell you?
And what does the vector space look like? Is it the span of those two vectors? Is this span minimal?

All the question says is to determine the basis. I am then given two column vectors (1,2) and (-1,1).

I solved the augmented matrix and obtained that both x1=0 and x2=0.

And what does x1 = 0 = x2 tell you? You are trying to determine if the two vectors are linearly independent, so you are solving the system (1,2)x2 + (-1,1)x2 = 0. Thus, a solution of (x1, x2) = (0, 0) tells you something about the vectors (1,2) and (-1,1).

I know they are independent from the det not equaling 0. I am trying to find the basis of the vector space.

What does the vector space look like? You have only identified two vectors. Is it the set of linear combinations of these two vectors?

I have giving you all the information. What are you asking for? It is in R^2 but that is also mentioned in the title.

vela
Staff Emeritus