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Let V be a vector space with basis B = {u, v}. Define T R² → V so that for all (a, b) E R² we have T(a, b): = : bu + av Consider the basis B' {(1, 2), (3, 4)} for R². What is the rank of T? Which one of the following statements is true? T' is ….. Using the given ordering of B and B', what is ([T] B‚ B') 22? =

Let V be a vector space with basis B = {u, v}. Define T R² → V so that for all (a, b) E R² we have T(a, b): = : bu + av Consider the basis B' {(1, 2), (3, 4)} for R². What is the rank of T? Which one of the following statements is true? T' is ….. Using the given ordering of B and B', what is ([T] B‚ B') 22? =

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section: Chapter Questions
Problem 16RQ
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Need help with this question. Please explain each step. The options for the second part are "linear and in injective but not surjective", "linear and surjective but not bijective", "bijective but not linear", "an isomorphism". Thank you :)

 

Let V be a vector space with basis B = {u, v}. Define T : R² → V so that for all (a, b) E R² we have T(a, b) = bu + av Consider the basis B' = {(1, 2), (3, 4)} for R². What is the rank of T? Which one of the following statements is true? T' is ….. Using the given ordering of B and B', what is ([T] B, B¹) 22?
Transcribed Image Text:Let V be a vector space with basis B = {u, v}. Define T : R² → V so that for all (a, b) E R² we have T(a, b) = bu + av Consider the basis B' = {(1, 2), (3, 4)} for R². What is the rank of T? Which one of the following statements is true? T' is ….. Using the given ordering of B and B', what is ([T] B, B¹) 22?
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