Answered: 5. Let U = {(u₁, U2, U3) E R³|u₁ + u2 -… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 42EQ

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5. Let U = {(u₁, U2, U3) € R³ | U₁ + U2 − u3 = 0} and V = {(V₁, V2, V3) € R³ | v₁ - 3v2 +5v3 = 0}.
(a) Show that U and V are subspaces of R³.
(b) Is the set U UV:= {x|x EU or x E V} a subspace of R³? Justify your answer.
(c) Is the set UnV:= {x|x EU and x E V} a subspace of R³? Justify your answer.

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Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 34. ,
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.
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.
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn,WAinMnn:detA=1

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