# Homework Help: Linear Algebra-question.

1. Oct 2, 2005

### iNCREDiBLE

Linear Algebra-question. HELP!!

Problem:

Let $L: R^3 \rightarrow R^4$ be a linear transformation that satisfies:
$L(e_1) = (2,1,0,1)^T = u$
$L(e_2) = (0,3,3,4)^T = v$
$L(e_3) = (2,-5,-6,-7)^T = w$.

Determine a base for $Range(L)$.

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Is the base $\{u,v\}$ since $w = u-2v$? Is it really that simple?

Last edited: Oct 2, 2005
2. Oct 2, 2005

### iNCREDiBLE

Help anyone??

Last edited: Oct 2, 2005
3. Oct 2, 2005

### iNCREDiBLE

4. Oct 2, 2005

yep.

there's a theorem saying that the basis of the range of a transformation is given by the set determined by the transformations of the vectors comprising the basis of the domain of the transformation.

and you used this and noted that the third vector is a linear combination of the other two...

so... yeah, you found the basis for the range of the transformation.