(a) Does the subset of all vectors with a₂ = 0 constitute a vector space? If so, what is its dimension; if not, why not? (b) What about the subset of all vectors whose z component is 1? (c) How about the subset of vectors whose components are all equal?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 40E
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Problem 3.1 Consider the ordinary vectors in three dimensions (axî + ayĵ + a₂k)
with complex components.
4A set of vectors that spans the space is also called complete, though I personally reserve that word
Transcribed Image Text:Problem 3.1 Consider the ordinary vectors in three dimensions (axî + ayĵ + a₂k) with complex components. 4A set of vectors that spans the space is also called complete, though I personally reserve that word
(a) Does the subset of all vectors with a₂ = 0 constitute a vector space? If so, what
is its dimension; if not, why not?
(b) What about the subset of all vectors whose z component is 1?
(c) How about the subset of vectors whose components are all equal?
Transcribed Image Text:(a) Does the subset of all vectors with a₂ = 0 constitute a vector space? If so, what is its dimension; if not, why not? (b) What about the subset of all vectors whose z component is 1? (c) How about the subset of vectors whose components are all equal?
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