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))

## kernel?

### Re: kernel?

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.

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.