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Math / Linear Algebra 4 / Chapter 2.1 / Problem 20

Linear Algebra | 4th Edition | ISBN: 9780130084514 | Authors: Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence

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Let V and W be vector spaces with subspaces Vi and Wi, respectively. If T: V W is

Chapter 2, Problem 20

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QUESTION:

Let V and W be vector spaces with subspaces Vi and Wi, respectively. If T: V W is linear, prove that. T(V() is a subspace of W and that {x V: T(x) Wi} is a subspace of V.

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QUESTION:

Let V and W be vector spaces with subspaces Vi and Wi, respectively. If T: V W is linear, prove that. T(V() is a subspace of W and that {x V: T(x) Wi} is a subspace of V.

ANSWER:

Step 1 of 2

Linear Transformation:

A function from one vector space to another that respects the underlying structure of each vector space. It is also defined as a linear operator or map.

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