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kernel?

Posted: Tue Jan 04, 2011 5:57 am
by hadimotamedi
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))

Re: kernel?

Posted: Thu Jan 06, 2011 12:58 am
by owlpride
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.