How Do You Prove Matrix Powers Using Mathematical Induction?

[rakileh]

Hey guys I am in precalculus right now and we just started picking up mathematical induction. Our teacher assigned us a problem that I am stumped over and I tried looking all over for a clear explanation online but I can't find anything remotely helpful. The question is:

Use mathematical induction to prove A = (2 0
0 3)^n = (2^n 0
0 3^n) for every positive integer n

Thank you!

 

[Kavik]

These are matrices, correct? Why not just try a couple examples of n, say n = 1. Then n = 2. Then n = 3. The pattern should be clear then and you could make a more general proof.

Matrix multiplication is all you need, e.g.: [A]^2 = [A]*[A]

 

[HallsofIvy]

Did you read the regulations that you agreed to abide by when you registered for this forum? You must make a valid attempt to solve the problem yourself and show your attempt here. Do you know how to multiply matrices? Do you know what "proof by induction" is?