Determine if a transformation is linear.

[thatguythere]

Homework Statement

Please see attached files and let me know if I am correct or not.

Homework Equations

The Attempt at a Solution

 

[Dick]

Homework Statement

Please see attached files and let me know if I am correct or not.

Homework Equations

The Attempt at a Solution

Can't say whether you are correct or not. You just wrote a bunch of stuff down. Are they linear or not?

 

[thatguythere]

What do you mean, I just wrote a bunch of stuff down? They are two separate transformations. I applied arbitrary vectors to them and attempted to prove if T(u+v) = T(u)+T(v) as well as T(cu)=cT(u)
In the first transformation, it appears that the first definition is not satisfied and in the second problem, the second definition is not satisfied. Therefore, I do not believe either are linear, however I am not certain if I am doing this properly.

 

[Dick]

What do you mean, I just wrote a bunch of stuff down? They are two separate transformations. I applied arbitrary vectors to them and attempted to prove if T(u+v) = T(u)+T(v) as well as T(cu)=cT(u)
In the first transformation, it appears that the first definition is not satisfied and in the second problem, the second definition is not satisfied. Therefore, I do not believe either are linear, however I am not certain if I am doing this properly.

That's exactly what I was asking for. I wanted to know your conclusions from what you wrote down. Correct that thay are both not linear. If you want to prove that just come up with specific examples of u, v and c (with numbers in them) where T(u+v)=T(u)+T(v) or T(cu)=cT(u) don't work.

 

[micromass]

Since when is 3^a + 3^b = 3^{a+b}?

 

[Dick]

Since when is 3^a + 3^b = 3^{a+b}?

That was my point. Just writing these things down doesn't say whether the poster believes them to be correct or incorrect. I'm not sure what writing a check next to it means.