kernel?

Forum for the GRE subject test in mathematics.
hadimotamedi
Posts: 34
Joined: Thu Dec 30, 2010 4:36 am

kernel?

Postby hadimotamedi » Tue Jan 04, 2011 5:57 am

Dear All
Can you please show me how the following lemma can be used to solve GRE math questions?
- dim E = dim f(E) + dim (E ∩ ker(f))

owlpride
Posts: 204
Joined: Fri Jan 29, 2010 2:01 am

Re: kernel?

Postby owlpride » Thu Jan 06, 2011 12:58 am

For example, the theorem tells you that the system of equations

x + y + z = 1
2x - y + 3 z = 4
x - 2y + 2z = 3

has a one-parameter family of solutions while the system

x + y + z = 1
2x - y + 3 z = 4
x - 3y + 2z = 3

has a unique solution.




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