Exercise 15.  Find the linear transformations    that satisfy the following conditions.  

15 (a).  The points    map onto  .

Solution 15 (a).

See text and/or instructor's solution manual.

Write out the two equations to solve:    for  .  

            

Solve the above system of equations.  Subtract equation 2 from equation 1.

            

Now solve for  A:

        .  
        
Then calculate  B:

          

The linear transformations is

          .  

The transformation     maps the points    map onto  .

We are done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

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