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?

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 66E
Question
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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