Pricing
Log in
Sign up
Home
Homework Help
Study Guides
Class Notes
Textbook Notes
Textbook Solutions
Booster Classes
Blog
Algebra
2
answers
0
watching
49
views
10 Nov 2019
A 7. (7 points) Let B(b,.. ., bn) be a basis for a vector space V. Show that the coordinate mapping x-? [X]B Is one-to-one. (You may not use the theorem that states this.)
For unlimited access to Homework Help, a
Homework+
subscription is required.
You have
0
free answers left.
Get unlimited access to
3.8 million
step-by-step answers.
Get unlimited access
Already have an account?
Log in
souravshit53
Lv6
17 Feb 2023
Unlock all answers
Get
1
free homework help answer.
Unlock
Already have an account?
Log in
You have
0
free answers left.
Get unlimited access to
3.8 million
step-by-step answers.
Get unlimited access
Already have an account?
Log in
Jean Keeling
Lv2
30 May 2019
Unlock
Already have an account?
Log in
Ask a question
Related questions
Let B = {b1, b2,... bn} be an ordered basis for vector space V. Show that every inner-product on V can be computed using the values ai, j = (bj|bi) i = 1,..., n, j = 1,..., n. Hint: Take x, y V and write them as linear combinations of bi's (i = 1,..., n). Form the inner prod (x|y) and the coordinates matrices of x and y in the ordered basis B, [x] B and [y] B. Show that (x|y) = [y] B A [x] B, where n times n matrix A = [ai, j] consists of the inner products of the vectors in ordered basis B.
Show transcribed image text
Let B = {b1, b2,... bn} be an ordered basis for vector space V. Show that every inner-product on V can be computed using the values ai, j = (bj|bi) i = 1,..., n, j = 1,..., n. Hint: Take x, y V and write them as linear combinations of bi's (i = 1,..., n). Form the inner prod (x|y) and the coordinates matrices of x and y in the ordered basis B, [x] B and [y] B. Show that (x|y) = [y] B A [x] B, where n times n matrix A = [ai, j] consists of the inner products of the vectors in ordered basis B.
orchidgnu700
JUST NEED PART C.
Consider the basis for R3 given by B= ((1,1,1), (0,1,1), (1,0,1)). (You do not need to prove that this is a basis.) Find the coordinate matrix [v]B for the vector v = (3,2,1) relative to the basis B. Find the vector w in R3 such that [w]B = Use your result in part (a) to deduce the coordinate matrix [v]c for the vector v = (3,2,1) relative to the basis C = ((1,0,1), (1,1,1), (0,1,1)).
Show transcribed image text
Consider the basis for R3 given by B= ((1,1,1), (0,1,1), (1,0,1)). (You do not need to prove that this is a basis.) Find the coordinate matrix [v]B for the vector v = (3,2,1) relative to the basis B. Find the vector w in R3 such that [w]B = Use your result in part (a) to deduce the coordinate matrix [v]c for the vector v = (3,2,1) relative to the basis C = ((1,0,1), (1,1,1), (0,1,1)).
maroongnat492
(8 points) Let V be a vector space of dimension n over the field R, and let B , , vn} be a basis of V. Define a map : V R" by letting s(v)-[u]B. Prove that Ï is an isomorphism, i.e., prove that Ï s linear, one-to-one, and onto.
Weekly leaderboard
Home
Homework Help
3,900,000
Algebra
190,000
Start filling in the gaps now
Log in
New to OneClass?
Sign up
Back to top
