A Linear Algebra Problem; functions

Question

[Problem on Linear Algebra How to approach the problem? I have no idea how to start with and solve.

Answer 1

From the information given, you should be able to construct formulas that give you $M_n$ and $A_n$ just from the value of $n$. The trick is to find the pattern that relates $n$ to the number of additions and multiplications performed. A good place to start is just to look at the ones that are apparent. Using the first four equations we can obtain: $$A_0=0, A_1=1, A_2=2, A_3=3$$ $$M_0=0, M_1=0, M_2=1, M_3=1$$