Let R be field and X= R³/s Vector space over RM=(a,b,c)labic, e Rra+b= 3- <3Show that Ms and why with proof.1) is convexset and affine set of botostii) is blanced set and symmetirs set of xiii) is hy per space and hyper plane ofx or hotiii) find f:MR st kerf = M 18/103and finnd fiM→R/{0} stM= {xEX, f(t) = x, texiαER?jiii) show that Mis Maxsubspace or notand Mis a max. affine set or not.

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Answered: Let R be field and X= R³/s Vector space…

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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True/ False Circle either "true" or "false" to indicate the veracity of each statement. You do NOT have to give any reasons for your answers. V. FALSE [1] For any functiom defined on vector spaces, p: (V, +;) → (V', +',') Dim(V) = Nullity ofo + Rank of o TRUE If o: (V, +,) → (V',+',') is a vector homomorphism, the Null Space ofo is a subspace of (V',+','). TRUE FALSE [2] If o: (V,+;) → (V', +',') is a vector homomorphism, the Range Space of o is a subspace of (V',+',;'). TRUE FALSE [3] If a : (V,+;) → (v', +',') and ß : (V, +,) → (V', +',') are two vector homomorphisms, then R(a) = R(B). FALSE [4] TRUE -> %3D If a : (V,+;) → (V', +',') and ß : (V,+;') → (V', +',') are two vector isomorphisms, then R(a) = R(B). TRUE FALSE [5] Suppose (V, +,) has a basis B =(ß1, B2 ), and we write B' = ( B2 B1) Let i be a vector in V. If Rep3(3) = then Reps, (5) = | FALSE [6] TRUE %3D VI. Circle the correct choice(s) in each problem. Here, assume is p a homomorphism. [1] Suppose p: M2x5 R° is surjective.…

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