SOLUTION: Define T : R^2 → R^2 by T(a1, a2) = (a1, −a2). Prove that T is linear, and find kernel and range of T.

Question 1182572: Define T : R^2 → R^2 by T(a1, a2) = (a1, −a2). Prove that T is linear, and find kernel and range of T.

Answer by ikleyn(52782) (Show Source): You can put this solution on YOUR website!
.


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.

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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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