Consider the identity function IN: N → N defined as IN (x) = x ∀ x ∈ N.Show that although IN is onto but IN + IN: N → N defined as(IN+ IN) (x) = IN(x) + IN(x) = x + x = 2x is not onto.
Consider the identity function IN: N → N defined as IN (x) = x ∀ x ∈ N.Show that although IN is onto but IN + IN: N → N defined as(IN+ IN) (x) = IN(x) + IN(x) = x + x = 2x is not onto.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 27EQ
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Consider the identity function IN: N → N defined as IN (x) = x ∀ x ∈ N.
Show that although IN is onto but
IN + IN: N → N defined as
(IN+ IN) (x) = IN(x) + IN(x) = x + x = 2x is not onto.
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