Originally Posted by

**shannon1111** I have no idea of this question, plz help me !~thanks

Let H be the span of the following six vextors:

V1=[1,-1,0,0]

V2=[1,0,-1,0]

V3=[1,0,0,-1]

v4=[0,1,-1,0]

v5=[0,1,0,-1]

v6=[0,0,1,-1]

1.Show that B={V1,V2,V3} is a basis for H .Do this by showing that (a) the vextors in B are independent, and (b) the remaining three vectors canbe each be expressed as a linear combination of vectors in B.

2. Find a different subset of the vectors that is still a basis for H.

3.Find a non-zero 1*4 matrix A such that Av=0 for all V in H