Determine whether the sets S, and S, span the same subspace of R°.S- {(0, 0, 1), (0, 1, 1), (2, 1, 1))S,- ((1,1, 1), (1, 1, 5), (5, 1, 1)}O S, and S., span the same subspace of R.O s, and S, do not span the same subspace of R.

Answered: Image /qna-images/answer/63107efc-9666-4075-975e-c8297c8fd3f9.jpg

Answered: Determine whether the sets S, and S,…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 24E: Spanning Sets In Exercise 19-24, determine whether the set Sspans R3. If the set does not span R3,...

See similar textbooks

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.
Spanning the Same Subspace In Exercises 61and 62, show that the sets S1and S2span the same subspace of R3. S1={(0,0,1),(0,1,1),(2,1,1)} S2={(1,1,1),(1,1,2),(2,1,1)}
Proof Prove that if S1 and S2 are orthogonal subspaces of Rn, then their intersection consists of only the zero vector.
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.
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.
Find the bases for the four fundamental subspaces of the matrix. A=[010030101].
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.
Spanning Sets In Exercise 19-24, determine whether the set Sspans R3. If the set does not span R3, then give a geometric description of the subspace that it does span. S={(1,0,3),(2,0,1),(4,0,5),(2,0,6)}
Calculus Repeat Exercise 45 for B={e2x,xe2x,x2e2x}. 45. Calculus Let B={1,x,ex,xex} be a basis for a subspace W of the space of continuous functions, and let Dx be the differential operator on W. Find the matrix for Dx relative to the basis B.
Calculus Let W1,W2,W3,W4, and W5 be defined as in Example 5. Show that Wi is a subspace of Wj for ij. Example 5 Subspaces of Functions Calculus Let W5 be the vector space of all functions defined on [0,1], and let W1,W2,W3, and W4 be defined as shown below. W1=setofallpolynomialfunctionsthataredefinedon[0,1]W2=setofallfunctionsthataredifferentiableon[0,1]W3=setofallfunctionsthatarecontinuouson[0,1]W4=setofallfunctionsthatareintegrableon[0,1]ShowthatW1W2W3W4W5andthatWiisasubspaceofWjforij.

SEE MORE QUESTIONS

Recommended textbooks for you

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

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

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Determine whether the sets S, and S, span the same subspace of R. S, = {(0, 0, 1), (0, 1, 1), (2, 1, 1)} S, = {(1, 1, 1), (1, 1, 5), (5, 1, 1)} %3D OS, and S, span the same subspace of R. O s, and S, do not span the same subspace of R.