Homework Help: Linear transformations formula

1. May 14, 2007

Aerosion

Linear transformations....

1. The problem statement, all variables and given/known data

Can't figure these things out for my life. Seriously. Here's an example.

consider the basis S={v1, v2, v3} for R^3 where v1=(1,2,1), v2=(2,9,0) and v3=(3,3,4) and let T:R^3-->R^2 be the linear transformation such that:

T(v1)=(1,0) T(v2)=(-1,1) T(v3)=(0,1)

Find formula for T(x1,x2,x3) and use it to find T(7,13,7)

2. Relevant equations

3. The attempt at a solution

So here I am starting it, writing c1(1,2,1)+c2(2,9,0)-C3(3,3,0) to make C1+2C2+3C3, 2C1+9C2+3C3, C1+C3

c1+2c2+3c3=x1
2c1+4c2+3c3=x2
c1+ +4c3=x3

Now, I'm having trouble solving for c1, c2, and c3. The answers seem to be c1=36x1+8x2+21x3, c2=5x1-x2-3x3, c3=9x1-2x2-5x3. I don't know where those numbers came from. (I was guessing putting it into a matrix and use row reduction, but...no). Hmm? Help?

2. May 14, 2007

Mindscrape

So the question is asking for the matrix that sends (1,2,1), ..., to their respective vectors in lR^2.

A v1 = ?
A v2 = ?
A v3 = ?

It seems like you are trying to find linear combinations of the vectors that will give the transformations. I don't think that is going to work.

If you can find the matrix that performs the transformations, you can use matrix multiplication to find the vectors corresponding to certain coordinates (c1,c2).

Last edited: May 14, 2007