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

In summary, the problem states that T is a linear transformation from R^3 to P2. T((1,1,-1))=X and T((1,0,-1))=X^2+7X-1 are given. It is asked to find T(0,-5,0) or explain why it cannot be determined from the given information. After some discussion, it is concluded that there is not enough information to determine T(0,-5,0) without knowing the formula for the transformation.
  • #1
iamzzz
22
0

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)
 
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  • #2
Saying that doesn't make it so. What have you tried?
 
  • #3
T((1,1,-1)) and T((1,0,-1)) should produce something close.
 
  • #4
True. So try something.
 
  • #5
i don't knwo :(
 
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  • #6
Hint: Can you build (0,-5,0) out of what you have?
 
  • #7
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
You didn't answer my question. Can you get (0,-5,0) or not?
 
  • #9
no The question did not give the formula of the transformation
 
  • #10
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
I am going to read textbook. Did not attend class Thanks for the hlep
 
  • #12
Frankly, you sound like you have never actually taken a course in linear algebra! Do you know what a "linear combination" of vectors is?
 

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

What is a linear transformation?

A linear transformation is a mathematical function that maps one vector space to another in a way that preserves the structure of the original vector space. It is also known as a linear map or linear operator.

How is a linear transformation represented?

A linear transformation can be represented by a matrix that contains the coefficients of the transformation. It can also be represented by a set of equations that describe how each element of the input vector is transformed.

What are the properties of a linear transformation?

Some common properties of a linear transformation are: it preserves the origin, it preserves addition and scalar multiplication, and it preserves the structure of the vector space (e.g. lines remain lines and planes remain planes).

How is a linear transformation applied to a vector?

To apply a linear transformation to a vector, you multiply the vector by the transformation matrix or plug the vector into the transformation equations. The resulting vector will be the transformed vector in the new vector space.

What are some real-life applications of linear transformations?

Linear transformations are used in many fields, including physics, engineering, computer graphics, and economics. Some examples of real-life applications include image and signal processing, geometric transformations in 3D computer graphics, and solving systems of linear equations in economics and business.

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