   Chapter 11.2, Problem 62E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# Discover: Powers of a Matrix Let A = [ 1 1 0 1 ] Calculate A 2 , A 3 , A 4 ,…. until you detect a pattern. Write a general formula for A n .

To determine

To calculate:

The matrices A2, A3, A4,…. and a general formula of An from the matrix A=.

Explanation

Approach:

Two matrices A and B can be multiplied if and only if the number of columns in A is same as the number of rows in B.

If A=[aij] is an m×n matrix and B=[bij] an n×k matrix, then their product in the m×k matrix C=[cij].

Calculation:

Consider the matrix A=.

The matrix operation A2 can be written as A×A. The product matrix A2 is given below.

A2==[11+1011+1101+1001+11]=

The matrix operation A3 can be written as A2×A. The product matrix A3 is given below.

A3==[11+2011+1201+1001+11]=

The matrix operation A4 can be written as A3×A

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