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# Proving a function is a linear map watch

1. The task is to prove that for all is a linear map.

This is my attempt:
https://imgur.com/a/JH4Bd

Is it correct or is something missing? (In my answer, I assumed the properties of addition and scalar multiplication given that being a ring.)
2. (Original post by MR1999)
The task is to prove that for all is a linear map.

This is my attempt:

Attachment 729810

Is it correct or is something missing? (In my answer, I assumed the properties of addition and scalar multiplication given that being a ring.)
So here s js just the zero map from R^n to R^n?
3. (Original post by MR1999)
The task is to prove that for all is a linear map.

This is my attempt:

Is it correct or is something missing? (In my answer, I assumed the properties of addition and scalar multiplication given that being a ring.)
4. Basically aU+bV is an element of R^n as R^n is a vector space and so it's always get mapped to 0n under s. It's trivial that this map is linear tbh.
You don't need to show the components of each of the vectors in R^n as we already know that R^n is indeed a vector space and the result just follows based on what it's means to be a vector space.
5. (Original post by B_9710)
Basically aU+bV is an element of R^n as R^n is a vector space and so it's always get mapped to 0n under s. It's trivial that this map is linear tbh.
The proof was rather easy but I feel like I might've missed something so I just want to make sure.
6. (Original post by RDKGames)
Try now
7. (Original post by MR1999)
Try now
Doesn't work.

8. (Original post by RDKGames)
Doesn't work.

I think I've got it fixed.
9. (Original post by MR1999)
I think I've got it fixed.
Yes your working is all good.

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