# Identify all linear transformations from C2 to C3

1. Oct 9, 2011

### jinksys

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

2. Relevant equations

3. The attempt at a solution

In the previous problem I was asked to identify if a polynomial, such as f(x)=2x was a linear transformation. In that case I checked to see if f(ax + by) = f(ax) + f(by). I figure I would be doing something similar in this case.

I would check to see if T(ax + by) = T(ax) + T(by).

So for problem (A) would I do something like:

and since T(ax + by) ≠ T(ax) + T(by), T1 is not a linear transformation?

2. Oct 9, 2011

### Bacle

You are correct, T1 is not a linear transformation, and your argument is correct/valid.

3. Oct 9, 2011

Thanks!

4. Oct 9, 2011

### jinksys

I have a question about part (D), which is

$$Tx = \left[ {\begin{array}{cc} 1 & 0 \\ 2-i & 3i \\ i-i & 4\\ \end{array} } \right]x$$

I assume I use the same procedure? Is anything special I need to do in regards to the complex variables?

I find that it IS a linear transformation, is that correct? Also, isn't i-i just 0?