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Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.(a) The set of all vectors mapped from a vector space V into another vector space W by a linear transformation T is the kernel of T.(b) The range of a linear transformation from a vector space V into a vector space W is a subspace of V.(c) The vector spaces R3 and M3,1 are isomorphic to each other.

Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.(a) The set of all vectors mapped from a vector space V into another vector space W by a linear transformation T is the kernel of T.(b) The range of a linear transformation from a vector space V into a vector space W is a subspace of V.(c) The vector spaces R3 and M3,1 are isomorphic to each other.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 48E
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Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.
(a) The set of all vectors mapped from a vector space V into another vector space W by a linear transformation T is the kernel of T.
(b) The range of a linear transformation from a vector space V into a vector space W is a subspace of V.
(c) The vector spaces R3 and M3,1 are isomorphic to each other.

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