See attached file.
Consider the relationship between the matrices A and B, explore the relationship between A and B and matrices representing other linear transformations derived from F and G. Explore 2 examples for example F+G for various  and , or the composite function FG/
Check that they are linear transformations then find the matrices representing them and see how they relate to A and B (the matrices representing F and G)
After some numerical work, make a general conjecture (analogous to the results stated in the theorem)© BrainMass Inc. brainmass.com October 9, 2019, 9:12 pm ad1c9bdddf
This shows how to make a conjecture using the relationship between transformation matrices.