Math Is Fun Forum

deepz

Member

Registered: 2007-03-20

Posts: 10

Linear Algebra

Hi I need help with the following questions:

State whether these are true or false with justification:

1) Every 18-dimensional vector space V contains a 8-dimensional subspace W

2) For all vectors v1,v2,v3,v4 which are elements of R8, span(v1+v2,v3+v4)= span(v1,v2,v3,v4)

3) There exists a 5x5 matrix whose characteristic polynomial is (x-1)^5 and minimal polynomial is x-6

Thanks in advance!

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Linear Algebra

Last edited by JaneFairfax (2008-12-01 23:08:32)

deepz

Member

Registered: 2007-03-20

Posts: 10

Re: Linear Algebra

I just wanted to ask a couple of things regarding the first 2 statements:

Does span(B') consist of 8 non-zero elements and 10 zeros?

And for the second statement, span(0,0)=span(v1,v2,v3,v4) where v2=-v1 and v4=-v3 as you said. So it is false unless v1=v2=v3=v4=0 is what you are saying?

I would really appreciate it if you could clarify this for me, thanks!