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1. Consider the vector space R2×3 and the subset b0] - {[6 8]₁4 | a,b=R}. H Show that H is a subspace of R²×3. -a

1. Consider the vector space R2×3 and the subset b0] - {[6 8]₁4 | a,b=R}. H Show that H is a subspace of R²×3. -a

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
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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1. Consider the vector space R²×3 and the subset b = { [ 2 ] LabER} a‚b≤R}. a, -a b H Show that H is a subspace of R²×3 2. Let H = {A € R³×3 | A is not invertible}. Show that H is not a subspace of the vector space R³×3. Note that it suffices to give one concrete example that violates one of the properties of a subspace. 3. Consider the vector space P3 of polynomial functions of degree at most 3. Let H = {ao+a₁t+ a₂t² + 1³ | ao, a₁, a2 € R}. Show that H is not a subspace of P3.
Transcribed Image Text:1. Consider the vector space R²×3 and the subset b = { [ 2 ] LabER} a‚b≤R}. a, -a b H Show that H is a subspace of R²×3 2. Let H = {A € R³×3 | A is not invertible}. Show that H is not a subspace of the vector space R³×3. Note that it suffices to give one concrete example that violates one of the properties of a subspace. 3. Consider the vector space P3 of polynomial functions of degree at most 3. Let H = {ao+a₁t+ a₂t² + 1³ | ao, a₁, a2 € R}. Show that H is not a subspace of P3.
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