Does S Span R^3? Determining Span and Linear Independence

[physics=world]

1. Determine whether the set a) spans r³ and b) is linearly independent.
S = {(1,0,0) , (0,1,0), (0,0,1), (2,-1,0)}

Homework Equations

3. For Span, I put it in a matrix:

1 0 0 2
0 1 0 -1
0 0 1 0

From there I concluded that the dimension of the column equal to the rank of the matrix, which is 3. So, it spans R³.

Is this right?

 

[tiny-tim]

hi physics=world!

… I concluded that the dimension of the column equal to the rank of the matrix, which is 3.

sorry, i don't understand …

can you please state this more clearly?​

(and anyway, isn't the answer obvious from looking at just the first three vectors?)