Question in shift linear: S:F_3[x]->F_3[x], T:F_3[x]->F_4[x], p(x) in...

[yossa]

Hello everyone, Need help with the following question please :
Be - F field. We will define duplicates - and - as follows:
for all - , and - .
Prove that S and T shift linear

 

[Dr.Peterson]

Hello everyone, Need help with the following question please :
Be - F field. We will define duplicates - View attachment 9672and - View attachment 9673 as follows:
for all - View attachment 9674, View attachment 9675 and - View attachment 9676.
Prove that S and T shift linear

These questions would be much easier to read if you just typed them. But also, you have clearly translated from another language, and your English is not standard. Here is what you are saying, as I read it:

Let F be a field. We will define mappings S:F₃[x]->F₃[x] and T:F₃[x]->F₄[x] as follows: For all p(x) \in F₃[x], S(p(x)) = p(x+1) and T(p(x)) = (x-1)p(x). Prove that S and T "shift linear".
​

Unfortunately, I don't know what "shift linear" means. Possibly it is "are linear transformations", but I don't think that's right.

Can you give us some help in interpreting this? Perhaps give us the original words for us to research, and show us the definitions of those terms as given to you.

Also, we want to see your own thinking. If you have no idea what to do, at least show the definition of "shift linear", which has to be the starting point, as your goal will be to show either that the functions fit the definition, or that some theorem applies.

 

[yossa]

These questions would be much easier to read if you just typed them. But also, you have clearly translated from another language, and your English is not standard. Here is what you are saying, as I read it:

Let F be a field. We will define mappings S:F₃[x]->F₃[x] and T:F₃[x]->F₄[x] as follows: For all p(x) \in F₃[x], S(p(x)) = p(x+1) and T(p(x)) = (x-1)p(x). Prove that S and T "shift linear".
​

Unfortunately, I don't know what "shift linear" means. Possibly it is "are linear transformations", but I don't think that's right.

Can you give us some help in interpreting this? Perhaps give us the original words for us to research, and show us the definitions of those terms as given to you.

Also, we want to see your own thinking. If you have no idea what to do, at least show the definition of "shift linear", which has to be the starting point, as your goal will be to show either that the functions fit the definition, or that some theorem applies.

First of all I'm really sorry for the incomprehensible English: /
The meaning of "shift" may be "copy, remove, displace, shift, transfer, crib"?
I do not yet have an edge or a thought about how to begin ....

 

[Dr.Peterson]

First of all I'm really sorry for the incomprehensible English: /
The meaning of "shift" may be "copy, remove, displace, shift, transfer, crib"?
I do not yet have an edge or a thought about how to begin ....

In order to determine what the word means mathematically, we need the mathematical definition. Please tell me how the concept was defined in your book. Translating one word does not help, because words are commonly used very differently in different contexts. But if you show us an entire paragraph of explanation that you were given, we will be able to see beyond the individual words. When language is an issue, the more you say, the better!

Also, as I suggested, it may help if you quote the problem (and the explanation of the term) in your original language, so that we can look up its meaning for ourselves. We may be better able to understand how to translate it than you are.