# Unknown Transformation Machine

1. May 5, 2015

### JoelN

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

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?

2. Relevant equations

What values/information is needed to calcuate T ?

3. 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 im still curious.
Maybe it cannot be solved or if it can its higher mathematics.

2. May 6, 2015

### 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?

3. May 6, 2015

### JoelN

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?

4. May 6, 2015

### ehild

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

5. May 6, 2015

### JoelN

only 2 vectors before and after going through T

6. May 6, 2015

### 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?

7. May 6, 2015

### HallsofIvy

Staff Emeritus
$R^4$ 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.

8. May 6, 2015

### JoelN

thanks to both.