Linear tranformations equality

[sphlanx]

Homework Statement

We are given a homogeneous system of 5 equations and 3 variables. We are asked to find the solutions (which i found to be unique and <0,0,0>) and then we are asked(along loads of other stuff:P):

a)If any two linear transformations g and f have kerf=kerg=<0,0,0> then they are equal.
b)If any two linear transformations g and f have imf=img=<0,0,0> then they are equal.

Homework Equations

The Attempt at a Solution

a) is wrong because there are infinite linear transformations with ker=<0,0,0> but different images. for (positive but not absolutely sure i am correct because the dimension of the images would be equal)
i think b) is correct but i am not sure. I would say that if imf=img=<0,0,0> then they are both the zero linear map so they are equal. Thanks again in advance

 

[rochfor1]

Sounds to me like you've got it down!