MHB Solve Vector Space Question: Get the Solution Now

LearnerJr
Messages
4
Reaction score
0
View attachment 6276

How do you solve this question I just need a solution
 

Attachments

  • image.jpeg
    image.jpeg
    18.8 KB · Views: 90
Physics news on Phys.org
Hello LearnerJr and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
greg1313 said:
Hello LearnerJr and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

Yes of course. For 2a I know a bit of indirect proof and assume the result
Is not true. But not sure still how to perceive this question in the long run.
2b I know if it's a basis it's vectors have to be linearly independent, they span V.but I still can't solve it.
 
Consider the equation $af(v_1)+ bf(v_2)+ cf(v_3)= 0$. In order to show that $f(v_1)$, $f(v_2)$, and $f(v_3)$ are independent we must show that a= b= c= 0.

Since f is a linear transformation, $af(v_1)+ bf(v_2)+ cf(v_3)= f(av_1+ bv_2+ cv_3)= 0$. Since the kernel of f is only the 0 vector, we must have $av_1+ bv_2+ cv_3= 0$. But we were given that $v_1$, $v_2$, and $v_3$ are independent so a= b= c= 0 as we wished.
 

Thread '##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?'

I asked online questions about Proposition 2.1.1: The answer I got is the following: I have some questions about the answer I got. When the person answering says: ##1.## Is the map ##\mathfrak{q}\mapsto \mathfrak{q} A _\mathfrak{p}## from ##A\setminus \mathfrak{p}\to A_\mathfrak{p}##? But I don't understand what the author meant for the rest of the sentence in mathematical notation: ##2.## In the next statement where the author says: How is ##A\to...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Similar threads

I Question about vector spaces and subsets
Replies
8
Views
3K
I About the definition of vector space of infinite dimension
Replies
18
Views
3K
I Two ways to define operations in a vector space
Replies
7
Views
2K
B Understanding Bases of a Vector Space
Replies
3
Views
3K
A What is a free product of groups or vector space?
Replies
2
Views
2K
A How to visualise complex vector spaces of dimension 2 and above
Replies
4
Views
3K
I General Linear Group GL(n) on Vector Spaces and canonical pairing invariance
Replies
1
Views
3K
I Dimension of a vector space and its subspaces
Replies
15
Views
4K
I Row space, Column space, Null space & Left null space
Replies
8
Views
3K
I Proving inequality about dimension of quotient vector spaces
Replies
25
Views
3K

Hot Threads

Recent Insights

Back
Top