Help me understand Linear Transformations?

May 2010
1
0
Hello everyone,
Right off the bat, I want you to know this is a course question. I'm not trying to get an easy answer or cheat in any way, I would just like to end this semester on a good note - knowing I at least halfway understand this item. The textbook's information doesn't seem to line up with what the question is asking and I'm very confused.

Any explanations, links to videos or websites or the like, would be a great help!

Question:

Which of the following are Linear Transformations:

(a): L(x,y,z) = (0,0)
(b): L(x,y,z) = (1,2,-1)
(c): L(x,y,z) = (x^2 + y, y-z)

I want to say that (a) is a Linear Transformation and (b) and (c) are not, but I honestly think that might be because (0,0) looks simple to me. :D

(Crying) Confused Newb
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
Hello everyone,
Right off the bat, I want you to know this is a course question. I'm not trying to get an easy answer or cheat in any way, I would just like to end this semester on a good note - knowing I at least halfway understand this item. The textbook's information doesn't seem to line up with what the question is asking and I'm very confused.

Any explanations, links to videos or websites or the like, would be a great help!

Question:

Which of the following are Linear Transformations:

(a): L(x,y,z) = (0,0)
(b): L(x,y,z) = (1,2,-1)
(c): L(x,y,z) = (x^2 + y, y-z)

I want to say that (a) is a Linear Transformation and (b) and (c) are not, but I honestly think that might be because (0,0) looks simple to me. :D

(Crying) Confused Newb
You need to verify if \(\displaystyle L(\alpha\mathbf{x}+\beta\mathbf{y})=\alpha L(\mathbf{x})+\beta L(\mathbf{y})\) \(\displaystyle \forall \mathbf{x},\mathbf{y}\in L\) and \(\displaystyle \alpha,\beta\in\mathbb{R}\). If that is the case, you have a linear transformations.