Linear Algebra (Vector Space)

Question

Determine whether s is a basis for the indicated vector space S= {(1,2),(1,-1)} for R² 

Answer 1

It's been a while, but I remember that a basis has the following characteristics:

 

1)  All basis vectors are linearly independent.

2)  The number of basis vectors is equal to the dimension of the vector space.

 

Linear independence is easy to verify for a set of 2 vectors.  If one vector is not a scalar multiple of the other, they are linearly independent. 

 

Regarding the second characteristic, what is the dimension of your vector space?  How many vectors are in S?