Answered: 3 1 and x2 = -2 2. Let S be the… | bartleby

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 26CR

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2

3
1
and x2 =
-2
2. Let S be the subspace of Rª spanned by x1 =
Find a basis for S-.
1

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Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Find the projection of the vector v=[102]T onto the subspace S=span{[011],[011]}.
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.
Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector space?
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.
Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Prove that the set of all singular 33 matrices is not a vector space.
АT (Ь — Ах) — ӧ. Interpret this statement in terms of the fundamental subspaces of A.
Compute the projection of (1, 1, 1) onto the subspace generated by (0, 1, 0) and (-4, 1, 3). Record the components of your answer as decimal numbers separated by commas. Save
Determine whether W is a subspace of V
Show that Null Space of Ax = 0 is a subspace.
Determine the dimension of the subspace H, where | | A = --:-

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