Question: The formula in Problem 29 can be used to compute A 2 without an explicit matrix multiplication. It follows that without an explicit matrix multiplication

The formula in Problem 29 can be used to compute A2 without an explicit matrix multiplication. It follows that


3 A = (a + d)A - (ad - bc)A


without an explicit matrix multiplication


image


and so on. Use this method to compute A2, A3, A4, and A5 given


image



Problems 28 through 30 develop a method of computing powers of a square matrix.



Problem 29


image


where I denotes the 2 x 2 identity matrix. Thus every 2 x 2 matrix A satisfies the equation


image

3 A = (a + d)A - (ad - bc)A

Step by Step Solution

★★★★★

3.46 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If A 2 1 12 A 4A31 4 A 4A3A A 4A3A then ad ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related First Course Differential Equations Questions!

Q:

Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...

Q:

Problems 28 through 30 develop a method of computing powers of a square matrix. If then show that where I denotes the 2 x 2 identity matrix. Thus every 2 x 2 matrix A satisfies the equation where det...

Q:

Cash budget. Jim Zeeman Clinic provided the financial information in Exhibit 5.14. Prepare a cash budget for the clinic for the quarter ending March 20X1. ANNEX 5.14 JIM ZEEMAN CLINIC Data Income and...

Q:

MAST20018 - Discrete Mathematics and Operations Research Assignment 3 Place in your tutor's box by 5pm Wednesday 5th October 2016 1. The following project consists of 8 activities, which have been...

Q:

only question 3 2. Consider the network below: (a) Write down the adjacency matrix for the given netw0rk using the formula. 1, if nodes 2' and j are connected by an edge A = [as]: at\": = . 01...

Q:

only question 3 2. Consider the network below: (a) Write down the adjacency matrix for the given netw0rk using the formula. 1, if nodes 2' and j are connected by an edge A = [as]: at\": = . 01...

Q:

2. Consider the network below: (a) Write down the adjacency matrix for the given netw0rk using the formula. 1, if nodes 2' and j are connected by an edge A = [as]: at\": = . 01 otherWISe. Index your...

Q:

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Q:

Please help with the following matrices questions: *Appreciate it if you can show your work If you are unable to view the questions below, here is link https://massey.limfinity.com/207/hillcipher.pdf...

Q:

12:38 4 Assignment Details MTH 154-N41A: Quantitative Reasoning (SP21) MTH 154 Excel Project In this major project, you will create an Excel file and answer questions about linear and exponential...

Q:

Refer to the temperature and precipitation data in Data Set 4 of Appendix B. Let the dependent variable be AVTEMP, and let the independent variables be those given in the exercise. (The data sets are...

Q:

Repeat Problem 6.3 with the following data (use Gs = 2.7): a. Determine the maximum dry unit weight of compaction and the optimum moisture content. Given: mold volume = 943.3 cm3. b. Determine the...