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.
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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Step 1
Let
defined as
So the standard matrix of is
Here is one to one because matrix A has three linearly independent column.
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