Recent content by 164694605

Here is my thinking, please help me to finish it, thank you! If these two vectors (1,-1,0) and (0,1,-1)will span R^3 then for each u=(u1,u2,u3) in R^3 there must be scalars c1 and c2, so that c1(1,-1,0)+c2(0,1,-1)=(u1,u2,u3) then i get u1=c1 u2=c2-c1 u3=-c2, which means there will be...

Exactly, as my previous post, I consider (x,-(x+z),z)=(1,-1,0)x+(0,-1,1)z which is more obvious that elements of B can be write as a linear combination of elements from A, but the question is how should I link these things into a proof? I can't just say because one is the linear combination of...

thanks for reply. I get the last part, but i have trouble to interpret it. this is what i have done so far: because x+y+z=0 so y=-(x+z) because the standard basis for R^3 is (1,0,0) (0,1,0) (0,0,1) so (x,y,z)=(x,-(x+z),z)=(1,0,0)x-(0,1,0)(x+z)+(0,0,1)z=(1,-1,0)x+(0,-1,1)z but the numbers...

hi guys, i have no idea of how to do the following question, could u give some ideas? Q:determine whether or not the given set forms a basis for the indicated subspace {(1,-1,0),(0,1,-1)}for the subspace of R^3 consisting of all (x,y,z) such that x+y+z=0 how should i start? i know the...