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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
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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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