Lesson: Power of a Matrix Mathematics

In this lesson, we will learn how to use the matrix multiplication to determine the square and cube of a square matrix.

Lesson Plan

Students will be able to

understand the notation of a matrix raised to a power and relate it to multiplication,
understand that only square matrices can be raised to a power,
find the square and cube of a given matrix,
find higher-order powers of matrices when there is a pattern for the multiplication,
perform operations on powers of matrices,
use the properties of matrix powers.

Q1:

Consider the matrix

Find .

Q2:

For write as a multiple of .

Q3:

Consider What is ?