Answered: 6. (a) Suppose U, W are subspaces of V.… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 10EQ

See similar textbooks

Related questions

Question

(please solve within 15 minutes for an upvote)

6. (a) Suppose U, W are subspaces of V. Show that (U + W)° = U°nW°.
(b) Suppose V is finite-dimensional and U and W are subspaces of V. Prove that (UnW)° = U° + W°.

Expert Solution

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector u=(1,1,1,1) in the form u=v+w, where v is in V and w is orthogonal to every vector in V.
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.
Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.
Suppose U and W are two-dimensional subspaces of R3. Show that U∩W≠{0}
Suppose U1; U2; :::; Um are Önite-dimensional subspaces of V .Prove thatU1 + U2 + ::: + Um is Önite-dimensionalanddim(U1 + U2 + ::: + Um) dim U1 + dim U2 + ::: + dim Um
Suppose V is finite-dimensional and U and W are subspaces of V with W^0 ⊂ U^0. Prove that U ⊂ W.
Let U and W be arbitrary subspaces in vector space V with dimensions dim U=6 and dimW=4. Which of the following conclusions is not correct? (a) If dimV=9, then dim(U∩W)≥1. (b) If dim(U∩W)=3, then dim(U+W)=7. (c) If dim(U+W)=6, then W⊆U. (d) If dim(U∩W)=4, then W⊆U. (e) If dimV=12, then U∩W={0}.
Suppose U and W are subspaces of V such that dimU=4, dimW=5, and dimV=7. Find thepossible dimensions of U∩W.
Show {s,t,4s-3t)|s and t are in ℝ} is a subspace of ℝ3.
If S and T are subspaces of V, then SintersectionT is a subspace. Select one: True False
What is the dimension of the sum of subspaces V and W in R^4, if V=span{(1,−1,0,1),(1,0,−1,1)} and W=span{(1,−2,1,1),(0,1,−1,0)}? (a) 0(b) 1.(c) 2.(d) 3.(e) 4

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS