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

15 (c).  The triangle with vertices    maps onto the triangle with vertices  ,  respectively.

Solution 15 (c).

See text and/or instructor's solution manual.

Write out the three equations to solve:    for  .  

            

Solve the above system of equations.  Subtract equation 1 from equations 2 and 3.

            

The system is consistent (equation 3 is equivalent to equation 2) and we see that  .  Use this fact to and solve for  B.

            

The linear transformations is

          .  

The transformation     maps the triangle with vertices  
onto the triangle with vertices  ,  respectively.

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