Determine which of the following are subspaces of R³. (The a, b, c below are some realnumbers).(a) The set W of all vectors of the form (a, b, c), where a = b - c.(b) The set W of all vectors of the form (a,0, c).(c) The set Wof all vectors of the form (a, 2a, 3a).(d) The set W of all vectors of the form (a, 1, a).

For being a subspace, the set must be closed under vector addition, closed under scalar…

Answered: 3. Determine which of the following are…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...

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Similar questions

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 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.
Consider the vector spaces P0,P1,P2,...,Pn where Pk is the set of all polynomials of degree less than or equal to k, with standard operations. Show that if jk, then Pj is the subspace of Pk.
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.
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={[a0a]}
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

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