Unknown Transformation Machine

[JoelN]

Homework Statement

You have a unknown Transformation machine T. that transforms from R^4 --> R^3

Vectors U and V are known and the output from T is also known.

Can You calculate the values of T?

Homework Equations

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What values/information is needed to calcuate T ?

The Attempt at a Solution

I can solve any Vector that is a linear combination of vectors U and/or V but the book doesn't say how to solve what T is and the problem doesn't need it either only to see if you can solve given vectors using linear comb of U and/or V but I am still curious.
Maybe it cannot be solved or if it can its higher mathematics.

 

[ehild]

The question you posed under "relevant equations" is not a relevant equation. How would you get the transformed vector if you knew the matrix components of the transformation? What are the dimensions of the transformation matrix T?

 

[JoelN]

The question you posed under "relevant equations" is not a relevant equation. How would you get the transformed vector if you knew the matrix components of the transformation? What are the dimensions of the transformation matrix T?

a R^4 --> R^3 Transformer is a 3X4 Matrix, i only know 2 values of 2 linearly independent vectors after going through T. Can i calculate T or do i need more information?

 

[ehild]

How many equations do you have for those 3x4 unknowns?

 

[JoelN]

How many equations do you have for those 3x4 unknowns?

only 2 vectors before and after going through T

 

[ehild]

You know what the transformation does with the subspace spanned by the given U and V vectors, but do not know what happens with the other vectors. Can you fully determine T?

 

[HallsofIvy]

$R^4$ has dimension 4 and u and v, even if they are independent can only span a subspace of dimension 2 (dimension 1 if they are dependent). You need to know what T, applied to two more independent vectors would give in order to completely determine T.

 

[JoelN]

You know what the transformation does with the subspace spanned by the given U and V vectors, but do not know what happens with the other vectors. Can you fully determine T?

$R^4$ has dimension 4 and u and v, even if they are independent can only span a subspace of dimension 2 (dimension 1 if they are dependent). You need to know what T, applied to two more independent vectors would give in order to completely determine T.

thanks to both.