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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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Question

Let W be the subspace of R* spanned by the vectors
and
1
4
Find the matrix A, relative to the standard basis {e1, e2, e3, e4}, of the orthogonal projection onto W.
A =

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Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn, W is the set of diagonal nn matrices
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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In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 34. ,
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[aba]}

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