Exercise 17.  Prove that the composition of two linear transformations is a linear transformation.  

Solution 17.

See text and/or instructor's solution manual.

Let  [Graphics:../Images/ComplexFunLinearModHome_gr_469.gif]  and  [Graphics:../Images/ComplexFunLinearModHome_gr_470.gif]  be two linear transformations.  Then  

        [Graphics:../Images/ComplexFunLinearModHome_gr_471.gif]  

which is the required form for a linear transformation.

 

 

This solution is complements of the authors.

 

(c) 2008 John H. Mathews, Russell W. Howell