9. Show thatS = {(x,y)|ax+by = 0, a, b real numbers}is a subspace of R².10. Let u₁= (3, -4,5) and u₂ = (-3, 14,-7).(a) Show that {u₁, u₂} forms a linearly independent set.(b) Construct an orthonormal basis {w₁, W2} for the subspace span{u₁, u₂} of R³.(c) Write u = (3, 6, 3) span{w₁, W2} as a linear combination of the orthonormal basisvectors found in (b). (Hint: Similar to the ideas in Theorem 7.7.1).

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Answered: is a subspace of R². S={(x,y)|ax+by =…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 42CR: 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...

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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.
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.
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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is a subspace of R². S={(x,y)|ax+by = 0, a, b real numbers}