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Suppose that T is a linear transformation from a vector space V to a vector space W. Furthermore, suppose that {61, 62, 63, 64} is a basis of V and {T(b¹),T(b²), T(b³),T(61)} is a basis of W. • What is the dimension of W? What is the dimension of the image of T"? ⚫ Why is T an isomorphism?

Suppose that T is a linear transformation from a vector space V to a vector space W. Furthermore, suppose that {61, 62, 63, 64} is a basis of V and {T(b¹),T(b²), T(b³),T(61)} is a basis of W. • What is the dimension of W? What is the dimension of the image of T"? ⚫ Why is T an isomorphism?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 43EQ
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Suppose that T is a linear transformation from a vector space V to a vector space W. Furthermore, suppose that {61, 62, 63, 64} is a basis of V and {T(b¹),T(b²), T(b³),T(61)} is a basis of W. • What is the dimension of W? What is the dimension of the image of T"? ⚫ Why is T an isomorphism?
Transcribed Image Text:Suppose that T is a linear transformation from a vector space V to a vector space W. Furthermore, suppose that {61, 62, 63, 64} is a basis of V and {T(b¹),T(b²), T(b³),T(61)} is a basis of W. • What is the dimension of W? What is the dimension of the image of T"? ⚫ Why is T an isomorphism?
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