Determine whether the set S spans R2. If the set does not span R2, then give a geometric description of the subspace that it does span.S = {(-2, 4), (4, –2), (2, 2)}O S spans R?.S does not span R2. S spans a line in R2.O s does not span R². S spans a point in R².

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Answered: Determine whether the set S spans R2.…

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...

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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.
Find the bases for the four fundamental subspaces of the matrix. A=[010030101].
Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.
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 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.
Proof Prove that if S1 and S2 are orthogonal subspaces of Rn, then their intersection consists of only the zero vector.
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.

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Determine whether the set S spans R2. If the set does not span R2, then give a geometric description of the subspace that it does span. S = {(-2, 4), (4, –2), (2, 2)}