3. a. Let T: V→R³ be a linear transformation from a vector space V to R¹. Geometrically, what are the possibilities for the range of T? b. Let T: R³W be a linear transformation from R¹ to a vec- tor space W. Geometrically, what are the possibilities for the kernel of T?

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
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Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 12CM
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33. a. Let T:V→R¹ be a linear transformation from a vector
space V to R³. Geometrically, what are the possibilities for
the range of T?
b. LetT : Rª – W be a linear transformation from R¹ to a vec-
tor space W. Geometrically, what are the possibilities for
the kernel of T?
Transcribed Image Text:33. a. Let T:V→R¹ be a linear transformation from a vector space V to R³. Geometrically, what are the possibilities for the range of T? b. LetT : Rª – W be a linear transformation from R¹ to a vec- tor space W. Geometrically, what are the possibilities for the kernel of T?
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