Let V be the vector space of all square sub-matrix over R. Examine whether or notw = (A: A E V, A² = A) is a subspace of V? Justify.

Let V be the vector space of all square sub-matrix over ℝ. Let , W = A / A∈V , A2 = A We need to…

Answered: Let V be the vector space of all square…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 28EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=M22,W={[abb2a]}

See similar textbooks

Similar questions

Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set {v12v2,2v23v3,3v3v1} linearly dependent or linearly independent? Explain.
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=M22,W={[abcd]:adbc}
Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many vectors are in a basis for the row space of A? c How many vectors are in a basis for the column space of A? d Which vector space Rk has the row space as a subspace? e Which vector space Rk has the column space as a subspace?
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[a0a]}
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=M22,W={[abb2a]}
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[aba+b+1]}
Find the bases for the four fundamental subspaces of the matrix. A=[010030101].
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[aba]}
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.
Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). 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.
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn, W is the set of diagonal nn matrices

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS

Let V be the vector space of all square sub-matrix over R. Examine whether or not W = (A: A E V, A² = A) is a subspace of V? Justify.