Finding T(0,-5,0) from Given Linear Transformation Values

[iamzzz]

Homework Statement

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.

Homework Equations

None

The Attempt at a Solution

There is only X given, and that 's not enough to fine T(0,-5,0)

 

[LCKurtz]

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

 

[iamzzz]

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

 

[LCKurtz]

True. So try something.

 

[iamzzz]

i don't knwo :(

 

[LCKurtz]

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

 

[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)

 

[LCKurtz]

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

 

[iamzzz]

no The question did not give the formula of the transformation

 

[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.

 

[iamzzz]

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

 

[HallsofIvy]

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