Exercise 5.6.9 Suppose T: R" → Rm is a linear transformation given by Tx=Ax where A is an m×n matrix. Show that T is never an isomorphism if m‡n. In particular, show that if m>n, T cannot be onto and if m
Exercise 5.6.9 Suppose T: R" → Rm is a linear transformation given by Tx=Ax where A is an m×n matrix. Show that T is never an isomorphism if m‡n. In particular, show that if m>n, T cannot be onto and if m
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 21EQ
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![Exercise 5.6.9 Suppose T: R" → Rm is a linear transformation given by
Tx=Ax
where A is an m ×n matrix. Show that T is never an isomorphism if m‡n. In particular, show that if
m>n, T cannot be onto and if m <n, then T cannot be one to one.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc77db10-411b-4277-b72e-b2214a4cc0f7%2F2106464e-5a12-42c0-826a-8f820249d150%2F9jbqdwf_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 5.6.9 Suppose T: R" → Rm is a linear transformation given by
Tx=Ax
where A is an m ×n matrix. Show that T is never an isomorphism if m‡n. In particular, show that if
m>n, T cannot be onto and if m <n, then T cannot be one to one.
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