I have a question here that asks to find a basis, which states:

Find a basis for V, where V = {T belongs to L(R²,R³)| T(1,2) = (0,0)}

Could anyone offer any ideas on how to tackle this question? I appreciate any help. Thanks.

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- Oct 21st 2009, 10:57 PMGreenDay14Finding a basis.
I have a question here that asks to find a basis, which states:

Find a basis for V, where V = {T belongs to L(R²,R³)| T(1,2) = (0,0)}

Could anyone offer any ideas on how to tackle this question? I appreciate any help. Thanks. - Oct 22nd 2009, 12:44 AMaman_cc
- Oct 22nd 2009, 05:52 AMHallsofIvy
Actually, the problem is not that there is not enough information but that what you give is contradictory. You say T is from to but then you say T((1, 2))= (0, 0) which is a transformation from to .

Is the subspace the set of all linear transformation from to such that T((1,2))= (0,0,0)? Or did you mean that T is from to ?

Assuming you meant the former, any linear transformation from to can be written as a matrix:

and your condition is

so you must have a+ 2b= 0, c+ 2d= 0, and e+ 2f= 0. Those, of course, give a= -2b, c= -2d, and e= -2f. The matrix can be written

.

If you mean to just follow the same ideas. - Oct 22nd 2009, 11:57 AMGreenDay14
aghh, thanks both of your for the help and I aplogize. Yes I did make a mistake, i meant for it to be T is from R² to R². Sorry again.

- Oct 22nd 2009, 12:07 PMaman_cc
- Oct 22nd 2009, 05:53 PMGreenDay14
I am very lost in this question lol.