<PRE><B>Question 1182572</B>
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&lt;pre&gt;

This map is the reflection of a coordinate plane about x-axis.


The kernel is 0 (zero; zero vector).


The range is the entire R^2, i.e. whole coordinate plane.



The fact that it is linear map is OBVIUOS; but you can check it formally on your own, 

if you know the definition of a linear map.
&lt;/pre&gt;

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Read your textbook.


Or you write your own, instead of reading the existing textbooks ?




By the way, what university are you and what is your Algebra textbook ?





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