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!

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- Apr 30th 2009, 07:00 PMantmanlinear transformation
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! - Apr 30th 2009, 07:10 PMThePerfectHacker
- May 1st 2009, 12:17 PMantman
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.

- May 1st 2009, 01:04 PMThePerfectHacker
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. - May 1st 2009, 01:11 PMantman
I understand that. Thank you! The way I did it is still correct then, just more work?

- May 1st 2009, 01:13 PMThePerfectHacker