Let T1: R3 -> R$ and T2: R$ -> R°. Give an explicit example (show me the matrices!!!) of T1 and T2 such that T, is one-to-one and T2 is onto, and T2 T, IS a bijection. Hint: for 6 and 7, you need only use ones and zeros in your examples - but you are free to be more creative, if you wish.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.5: Applications
Problem 30EQ
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Let T1: R3 -> R$ and T2: R5 -> R3. Give an explicit example (show me the matrices!!!) of
T1 and T2 such that Ti is one-to-one and T2 is onto, and T2 T, IS a bijection. Hint: for 6 and 7,
you need only use ones and zeros in your examples - but you are free to be more creative, if
you wish.
Transcribed Image Text:Let T1: R3 -> R$ and T2: R5 -> R3. Give an explicit example (show me the matrices!!!) of T1 and T2 such that Ti is one-to-one and T2 is onto, and T2 T, IS a bijection. Hint: for 6 and 7, you need only use ones and zeros in your examples - but you are free to be more creative, if you wish.
Expert Solution
Step 1

Let 

                   T1:R3R5 

defined as

                  T1(x1, x2,x3)=x1, x2, x3, 0x4, 0x5

So the standard matrix of T1 is

                       A=100010001000000

Here T1 is one to one because matrix A has three linearly independent column. 

 

                   

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