True or false?(1)If x, y and z are vectors in an inner product space such that (x, y) = (x, z),then y = 2.(ب)If (x, y) = 0 for all ä in an inner product space, then y = 0.

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Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 5CM: Take this test to review the material in Chapters 4 and 5. After you are finished, check your work...

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Similar questions

Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1) is a vector space. If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.
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.
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.
Prove the parallelogram law on an inner product space V; that is, show that ||x+y||² + ||x-y||² = 2||x||² + 2||y||² for all x,y ϵ V. What does this equation state about parallelograms in R² ?
Prove the parallelogram law on an inner product space V; that is, show that ||x + y||2 + ||x −y||2= 2||x||2 + 2||y||2for all x, y ∈V.What does this equation state about parallelograms in R2?
How does the concept of duality benefit the study of linear spaces, especially in relation to basis and dual basis vectors?
Does the set of all functions that vanish at x = 0 and x = L form a vector space? If it does, explicitly show that it satisfies all eight properties required of a vector space. If not, which property fails? Show how it fails.

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If x, y and z are vectors in an inner product space such that (x, y) = (x, z), then y = 2.