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Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 73CR

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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, –2), (-1,2)}
O S spans R2.
O s does not span R. S spans a line in R.
O s does not span R. S spans a point in R.
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Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of 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.
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Which vector spaces are isomorphic to R6? a M2,3 b P6 c C[0,6] d M6,1 e P5 f C[3,3] g {(x1,x2,x3,0,x5,x6,x7):xiisarealnumber}
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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