Let be the linear transformation defined by
a) Is in ker L?
b) Is in ker L?
c) Is in range L?
c) Is in range L?
Thank you for your help!
For range, I would just have to find a vector v such that L(v)=w, so w is in the range of L. So a is not in kernel L but b is and c is in range L but d is not? For the range, I set up a 2x3 matrix with the vector in question as column 3 then found rref. Is this correct? d would not be in range because in the reduced matrix -1 does not equal 0.
Notice that .
Thus, to be in the range it needs to be a linear combination of .
There are of course many other ways to solve this problem, I just happen to like the approach that uses linear combinations. I looks like that approach uses least amount of computation since these are just matrices.