menu
QAmmunity.org
Login
Register
My account
Edit my Profile
Private messages
My favorites
Ask a Question
Questions
Unanswered
Tags
Categories
Ask a Question
So here is a theoretical question. Let L1 and L2 be linear transformation from a vector space V into Vector space W. Let {v1,v2,....,vn} be a basis for V. Show that if L1(vi)=L2(vi) for i=1,2,....,n then
asked
Jul 22, 2017
48.4k
views
4
votes
So here is a theoretical question. Let L1 and L2 be linear transformation from a vector space V into Vector space W. Let {v1,v2,....,vn} be a basis for V. Show that if L1(vi)=L2(vi) for i=1,2,....,n then L1(v)=L2(v) for any v in V. ...?
Mathematics
high-school
Ed Ayers
asked
by
Ed Ayers
8.1k
points
answer
comment
share this
share
0 Comments
Please
log in
or
register
to add a comment.
Please
log in
or
register
to answer this question.
1
Answer
6
votes
if v belongs to V, then we can find scalars a1,a2,...,an, such that v=a1*v1+a2*v2+...+an*vn, L1(v)=L1(a1*v1+a2*v2+...+an*vn) =a1*L1(v1)+a2*L1(v2)+...+an*L1(vn) =a1*L2(v1)+a2*L2(v2)+...+an*L2(vn) =L2(a1*v1+a2*v2+...+an*vn) =L2(v)
P Ackerman
answered
Jul 27, 2017
by
P Ackerman
8.2k
points
ask related question
comment
share this
0 Comments
Please
log in
or
register
to add a comment.
← Prev Question
Next Question →
Related questions
asked
Dec 28, 2024
72.1k
views
CFLs are closed under union If L1 and L2 are CFLs, then L1 ∪ L2 is a CFL. Proof 1. Let L1 and L2 be generated by the CFG, G1 = (V1, T1, P1, S1) and G2 = (V2, T2, P2, S2), respectively. 2. Without loss
Giavac
asked
Dec 28, 2024
by
Giavac
8.1k
points
Mathematics
high-school
1
answer
5
votes
72.1k
views
asked
Nov 11, 2024
23.5k
views
prove that if s = {v1, v2, ⋯, vn} is a basis for a vector space v and c is a nonzero scalar, then the set s1 = {cv1, cv2,⋯ , cvn} is also a basis for v.
Srfrnk
asked
Nov 11, 2024
by
Srfrnk
8.6k
points
Mathematics
high-school
1
answer
5
votes
23.5k
views
asked
Dec 28, 2021
64.9k
views
Use mathematical induction to prove that if L is a linear transformation from V to W, then L (α1v1 + α2v2 +· · ·+αnvn)= α1L (v1) + α2L (v2)+· · ·+αnL (vn) g
Nauman Umer
asked
Dec 28, 2021
by
Nauman Umer
7.7k
points
Mathematics
college
2
answers
0
votes
64.9k
views
Ask a Question
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.
9.4m
questions
12.2m
answers
Other Questions
What is .725 as a fraction
How do you estimate of 4 5/8 X 1/3
A bathtub is being filled with water. After 3 minutes 4/5 of the tub is full. Assuming the rate is constant, how much longer will it take to fill the tub?
i have a field 60m long and 110 wide going to be paved i ordered 660000000cm cubed of cement how thick must the cement be to cover field
Write words to match the expression. 24- ( 6+3)
Twitter
WhatsApp
Facebook
Reddit
LinkedIn
Email
Link Copied!
Copy
Search QAmmunity.org