# Linear transformation

1. Dec 16, 2012

### iamzzz

1. The problem statement, all variables and given/known data
You are given that T is a linear transformation from R^3 to P2, that T((1,1,-1))
=X, and that T((1,0,-1))=X^2+7X-1. Find T(0,-5,0) or explain why it cannot be determined form the given information.

2. Relevant equations
None

3. The attempt at a solution
There is only X given, and that 's not enough to fine T(0,-5,0)

2. Dec 16, 2012

### LCKurtz

Saying that doesn't make it so. What have you tried?

3. Dec 16, 2012

### iamzzz

T((1,1,-1)) and T((1,0,-1)) should produce something close.

4. Dec 16, 2012

### LCKurtz

True. So try something.

5. Dec 16, 2012

### iamzzz

i dont knwo :(

Last edited: Dec 16, 2012
6. Dec 16, 2012

### LCKurtz

Hint: Can you build (0,-5,0) out of what you have?

7. Dec 16, 2012

### iamzzz

C1*(1,1,-1)+c2(1,0,-1)
C1=-5 and C2=5

-5(1,0,1)+5(1,7,-1)=(5,30,-5)

8. Dec 16, 2012

### LCKurtz

You didn't answer my question. Can you get (0,-5,0) or not?

9. Dec 16, 2012

### iamzzz

no The question did not give the formula of the transformation

10. Dec 16, 2012

### LCKurtz

Like I said above, stating it doesn't make it so. It looks like you are just guessing in post #7. You need to show why you can or can not get (0,-5,0) that way.

11. Dec 16, 2012

### iamzzz

I am going to read textbook. Did not attend class Thanks for the hlep

12. Dec 17, 2012

### HallsofIvy

Staff Emeritus
Frankly, you sound like you have never actually taken a course in linear algebra! Do you know what a "linear combination" of vectors is?