Linear Algebra and Its Applications, 5th Edition
Authors: David C. Lay, Steven R. Lay, Judi J. McDonald
ISBN-13: 978-0321982384
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See our solution for Question 34E from Chapter 1.9 from Lay's Linear Algebra and Its Applications, 5th Edition.
Problem 34E
Chapter:
Problem:
Why is the question “Is the linear transformation T onto?” an existence question?
Step-by-Step Solution
Given Information
We have to prove that why is the question “Is the linear transformation T onto?” an existence question?
Step-1:
Let, T maps from $R^n$ to $R^m$. Then if the transformation is onto then it represents the existence of a vector x in $R^n$ such that $T(x)=b$, for each vector b in $R^m$. Therefore,
The asked question is an existence question
We have to prove that why is the question “Is the linear transformation T onto?” an existence question?
Step-1:
Let, T maps from $R^n$ to $R^m$. Then if the transformation is onto then it represents the existence of a vector x in $R^n$ such that $T(x)=b$, for each vector b in $R^m$. Therefore,
The asked question is an existence question