A spanning set for a (sub-) space is a set of elements of which spans . A set spans if for all is a linear combination of elements of .

This is the standard basis for , so spans .Then please show me how to do the below questions. Thank you very much.

Determine whether any of the following sets are spanning sets for R^2 , considered as column matrices

1) S = { esub1 = [1] , esub2 = [0]}

........................[0]............. [1]

This contains the standard basis and so spans2) S = { esub1 = [1] , esub2 = [0], fsub1 = [1]}

........................[0]............. [1].............[1]

cannot be written as a linear combination of elements of , so does not span .3) S = { fsub1 = [1] , fsub2 = [2]}

.......................[1]............. [2]

RonL