a) Let V = R' and let W = {(a,b,c) e R° | a² +b² +c² = 0} . Is W a subspace of V ? Justify your answer. and let W = {A €V|tr(A)#0}. Is W a subspace of V ? Justify your answer. . c) Let V = R' and let W = {(x, y, z) eR° | x= 3y} . Is W a subspace of V ? If it is, find a basis and b) Let V = M %3D 3x3 dimension for this subspace.

a) Let V = R' and let W = {(a,b,c) e R° | a² +b² +c² = 0} . Is W a subspace of V ? Justify your answer. and let W = {A €V|tr(A)#0}. Is W a subspace of V ? Justify your answer. . c) Let V = R' and let W = {(x, y, z) eR° | x= 3y} . Is W a subspace of V ? If it is, find a basis and b) Let V = M %3D 3x3 dimension for this subspace.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 67E: Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many...

See similar textbooks

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.
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?
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.
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. 34. ,