- #1

mitch_1211

- 99

- 1

I can prove that for eg if {v1,v2,v3} is a basis then {u1,u2,u3} is a basis where u1=v1 u2=v1+v2, u3=v1+v2+v3

I setup the equation c1(u1)+c2(u2)+c3(u3)=0 and determine if the only solutions are c1=c2=c3=0 or if there are others. This then gives linear independence or dependence and because there are the right number of vectors (3 u's and 3v's) spanning will automatically follow if vectors are linearly independent.

I'm not sure how to approach the matrix basis case...