Which of these transformations are linear?

[mahrap]

$$y_{1}=2x_{2}$$
$$y_{2}=x_{2}+2$$
$$y_{3}=2x_{2}$$

I know that in order for a transformation to be linear it has to satisfy:

I) $$T(v + w) = T(v) + T(w)$$
II) $$T(kv) = kT(v)$$

But what are v and w in this case?

note: v and w are vectors and are suppose to have arrows on top of them but I was too lazy to figure out how to type this out :P

 

[Mark44]

$$y_{1}=2x_{2}$$
$$y_{2}=x_{2}+2$$
$$y_{3}=2x_{2}$$

I know that in order for a transformation to be linear it has to satisfy:

I) $$T(v + w) = T(v) + T(w)$$
II) $$T(kv) = kT(v)$$

But what are v and w in this case?

v and w are vectors in the domain of the transformation. Presumably they would look like this:
$$ v = \begin{bmatrix} v_1 \\ v_2\end{bmatrix}$$
$$ w = \begin{bmatrix} w_1 \\ w_2\end{bmatrix}$$

Is there information in the problem you haven't provided? When you post a problem, you need to provide the complete problem statement. Also, the three parts of the template are there for a reason - don't just delete them.

note: v and w are vectors and are suppose to have arrows on top of them but I was too lazy to figure out how to type this out :P

 

[mahrap]

v and w are vectors in the domain of the transformation. Presumably they would look like this:
$$ v = \begin{bmatrix} v_1 \\ v_2\end{bmatrix}$$
$$ w = \begin{bmatrix} w_1 \\ w_2\end{bmatrix}$$

Is there information in the problem you haven't provided? When you post a problem, you need to provide the complete problem statement. Also, the three parts of the template are there for a reason - don't just delete them.

Sorry about the formatting. I'll keep that in mind the next time I post. However, I did not leave out any parts of the problem. The problem simply asked which of these transformations are linear and then provided the 3 equations given.

 

[Mark44]

Do you have enough information to start the problem now?