Homework Answers
Add Answer to:
6. Let E and F be subspaces of a vector space V. Prove that: (a) EUF...
just part c,d, and e please!! Let V be a finite-dimensional vector space over F. For...
just part c,d, and e please!!
Let V be a finite-dimensional vector space over F. For every subset SCV, define Sº = {f eV" f(s) = 0 Vs ES}. (a) Prove that sº is a subspace of V* (S may not be a subspace!) (b) If W is a subspace of V and r & W, prove that there exists an few with f(x) +0. (c) If v inV, define u:V* → F by 0(f) = f(v). (This is linear...
a. Let W and X both be subspaces of a vector space V. Prove that dim(WnX)...
a. Let W and X both be subspaces of a vector space V. Prove that dim(WnX) > dim(W) + dim(X) - dim(V) b. Define a plane in R" (as a vector space) to be any subspace of dimension 2, and a line to be any subspace of dimension 1. Show that the intersection of any two planes in R' contains a line. c. Must the intersection of two planes in R* contain a line?
Let V be a finite-dimensional vector space over F. For every subset SCV, define Sº =...
Let V be a finite-dimensional vector space over F. For every subset SCV, define Sº = {f EV* | f(s) = 0 Vs E S}. (a) Prove that sº is a subspace of V* (S may not be a subspace!) (b) If W is a subspace of V and x € W, prove that there exists an fe Wº with f(x) + 0. (c) If v inV, define û :V* + F by ū(f) = f(u). (This is linear and...
Problem 6. Let V be a vector space (a) Let (--) : V x V --> R be an inner product. Prove that (-, -) is a bilinear f...
Problem 6. Let V be a vector space (a) Let (--) : V x V --> R be an inner product. Prove that (-, -) is a bilinear form on V. (b) Let B = (1, ... ,T,) be a basis of V. Prove that there exists a unique inner product on V making Borthonormal. (c) Let (V) be the set of all inner products on V. By part (a), J(V) C B(V). Is J(V) a vector subspace of B(V)?...
1 Problem 4. Let V be a vector space and let U and W be two subspaces of V. Let (1) Prove that ifU W andWgU then UUW is not a subspace of V (2) Give an example of V, U and W such that U W andWgU. Expl...
1
Problem 4. Let V be a vector space and let U and W be two subspaces of V. Let (1) Prove that ifU W andWgU then UUW is not a subspace of V (2) Give an example of V, U and W such that U W andWgU. Explicitly verify the implication of the statement in part1). (3) Proue that UUW is a subspace of V if and only if U-W or W- (4) Give an example that proues the...
Let W1 and W, be the subspaces of a vector space V. Show that WinW, is...
Let W1 and W, be the subspaces of a vector space V. Show that WinW, is a subspace of V.
Problem #6. Let V be a finite dimensional vector space over a field F. Let W...
Problem #6. Let V be a finite dimensional vector space over a field F. Let W be a subspace of V. Define A(W) e Vw)Vw E W). Prove that A(W) is a subspace of (V).
Problem 4. Let V be a vector space and let U and W be two subspaces...
Problem 4. Let V be a vector space and let U and W be two subspaces of V. Let (1) Prove that if U g W and W g U then UUW is not a subspace of V 2) Give an ezample of V, U and W such that U W andW ZU. Explicitly verify the implication of the statement in part (1) (3) Prove that UUW is a subspace of V if and only ifUCW or W CU.' (4)...
please help me,thanks! 3. Let Fo be a field with 9 elements. Consider the set S () e Fo] deg(f()) 18, f( f(1) (2)) (4) 0 and (a) Compute IS. (b) Prove that S is a vector space over F (c) Compute...
please help me,thanks!
3. Let Fo be a field with 9 elements. Consider the set S () e Fo] deg(f()) 18, f( f(1) (2)) (4) 0 and (a) Compute IS. (b) Prove that S is a vector space over F (c) Compute dimF, S Let V be a vector space over F. Prove that X C V is a subspace if and only if v, w E X implies av+wEX for every aEF
3. Let Fo be a field with...
2. On subspaces of C(-1,1) Let V C(-1,1) be the vector space of all continuous real...
2. On subspaces of C(-1,1) Let V C(-1,1) be the vector space of all continuous real valued functions on on the interval (-1, 1), with usual addition and scalar multiplication. (a) Verify, if the set W-f eV: f(0)-0is a subspace of V or not? (b) Verify, if the set W-Uev f(0) 1 is a subspace of V or not? (c) Verify, if the set W-İfEV:f(x)-0V-2-z is a subspace of V or not? 1b) PrtScn Home FS F6 F7 F8 5
just part c,d, and e please!!
Let V be a finite-dimensional vector space over F. For every subset SCV, define Sº = {f eV" f(s) = 0 Vs ES}. (a) Prove that sº is a subspace of V* (S may not be a subspace!) (b) If W is a subspace of V and r & W, prove that there exists an few with f(x) +0. (c) If v inV, define u:V* → F by 0(f) = f(v). (This is linear...
a. Let W and X both be subspaces of a vector space V. Prove that dim(WnX) > dim(W) + dim(X) - dim(V) b. Define a plane in R" (as a vector space) to be any subspace of dimension 2, and a line to be any subspace of dimension 1. Show that the intersection of any two planes in R' contains a line. c. Must the intersection of two planes in R* contain a line?
Let V be a finite-dimensional vector space over F. For every subset SCV, define Sº = {f EV* | f(s) = 0 Vs E S}. (a) Prove that sº is a subspace of V* (S may not be a subspace!) (b) If W is a subspace of V and x € W, prove that there exists an fe Wº with f(x) + 0. (c) If v inV, define û :V* + F by ū(f) = f(u). (This is linear and...
Problem 6. Let V be a vector space (a) Let (--) : V x V --> R be an inner product. Prove that (-, -) is a bilinear form on V. (b) Let B = (1, ... ,T,) be a basis of V. Prove that there exists a unique inner product on V making Borthonormal. (c) Let (V) be the set of all inner products on V. By part (a), J(V) C B(V). Is J(V) a vector subspace of B(V)?...
1
Problem 4. Let V be a vector space and let U and W be two subspaces of V. Let (1) Prove that ifU W andWgU then UUW is not a subspace of V (2) Give an example of V, U and W such that U W andWgU. Explicitly verify the implication of the statement in part1). (3) Proue that UUW is a subspace of V if and only if U-W or W- (4) Give an example that proues the...
Let W1 and W, be the subspaces of a vector space V. Show that WinW, is a subspace of V.
Problem #6. Let V be a finite dimensional vector space over a field F. Let W be a subspace of V. Define A(W) e Vw)Vw E W). Prove that A(W) is a subspace of (V).
Problem 4. Let V be a vector space and let U and W be two subspaces of V. Let (1) Prove that if U g W and W g U then UUW is not a subspace of V 2) Give an ezample of V, U and W such that U W andW ZU. Explicitly verify the implication of the statement in part (1) (3) Prove that UUW is a subspace of V if and only ifUCW or W CU.' (4)...
please help me,thanks!
3. Let Fo be a field with 9 elements. Consider the set S () e Fo] deg(f()) 18, f( f(1) (2)) (4) 0 and (a) Compute IS. (b) Prove that S is a vector space over F (c) Compute dimF, S Let V be a vector space over F. Prove that X C V is a subspace if and only if v, w E X implies av+wEX for every aEF
3. Let Fo be a field with...
2. On subspaces of C(-1,1) Let V C(-1,1) be the vector space of all continuous real valued functions on on the interval (-1, 1), with usual addition and scalar multiplication. (a) Verify, if the set W-f eV: f(0)-0is a subspace of V or not? (b) Verify, if the set W-Uev f(0) 1 is a subspace of V or not? (c) Verify, if the set W-İfEV:f(x)-0V-2-z is a subspace of V or not? 1b) PrtScn Home FS F6 F7 F8 5
Most questions answered within 3 hours.
-
The pH of a sample of water from a river is 5.0. A
sample of effluent from...
asked 35 minutes ago -
At the beginning of the period, the Fabricating Department
budgeted direct labor of $136,500 and equipment...
asked 1 hour ago -
Please answer all
____ 28. Rent control is usually
justified on the grounds that it protects...
asked 1 hour ago -
PARTS A-D HAVE BEEN ANSWERED. WAS TOLD TO REPOST. ONLY ANSWER
PARTS E and F.
A...
asked 1 hour ago -
2) You are given the task of finding a representation for a
circle in a drawing...
asked 2 hours ago -
STUDY QUESTION: Does use of diet drug fen-phen
(fenfluramine-phentermine) cause valvular heart disease?
HINT: Valvular heart...
asked 2 hours ago -
1. An object weighing 40 N rests on a surface. The coefficient
of friction is 0.35....
asked 3 hours ago -
Investor company owns 35% of investee company voting stock and
accounts for the investment under the...
asked 4 hours ago -
The number of major faults on a randomly chosen 1 km stretch of
highway has a...
asked 5 hours ago -
Consider the competitive environment of Starbuck's, Progressive
Insurance, a manufacturing firm with low turnover, or a...
asked 5 hours ago -
3. Gains from trade
Consider two neighbouring island countries called Euphoria and
Contente. They each have...
asked 7 hours ago -
A business executive has the option to invest money in two
plans: Plan A guarantees that...
asked 10 hours ago