Example 1

In this video I show you how to use mathematical induction to prove matrix multiplication problems.

Prove the following:

  1. {\text{If }}M = \left( {\begin{array}{*{20}{c}} 1&0\\ 3&1 \end{array}} \right) \\ \\ \\ {\text{Prove that }}{M^n} = \left( {\begin{array}{*{20}{c}} 1&0\\ {3n}&1 \end{array}} \right)\hphantom{a}{\text{ where }}n{\text{ is a positive integer}}

The method of induction:

  • Start by proving that it is true for n=1, then assume true for n=k and prove that it is true for n=k+1. If so it must be true for all positive integer values of n.

Example 2

In this video I show you how to use mathematical induction to prove matrix multiplication problems.

Prove the following:

  1. {\text{If }}A = \left( {\begin{array}{*{20}{c}} 3&{ - 1}\\ 4&{ - 1} \end{array}} \right). \\ \\ \\ {\text{Prove that }}{A^n} = \left( {\begin{array}{*{20}{c}} {2n + 1}&{ - n}\\ {4n}&{1 - 2n} \end{array}} \right){\text{ where }}n{\text{ is a positive integer}}