My tips for Assignment 4 are coming below, but first a couple of announcements.

 

Please note that my final exam prep seminar for Math 1300 will be on Sunday, Dec. 9, in room 100 St. Paul's College, from 9 am to 9 pm .  For complete info about the seminar, and to register if you have not done so already, click this link:

I am also offering seminars in Calculus, Stat 1000, and Stat 2000 in the coming weeks.  You can get info about those seminars here:

Grant's One-Day Exam Prep Seminars

 

You will need to study Lesson 3 (Matrix Math), Lesson 4 (Inverse Matrices), Lesson 5 (Elementary Matrices), and Lesson 14 (Markov Analysis) to prepare for assignment 4.

 

Question 3 is just finding an inverse matrix by row-reduction as taught in Lesson 4 of my book.  Note that when they ask you to verify your answer, they want you to show that A*A-inverse = I.  Compute the product of your inverse matrix and the original matrix A, and show the answer is a 4 by 4 identity matrix.

 

Question 4 is more inverse matrix stuff.  In part (a), they mean write the coefficient matrix A times the variable matrix X = the constant matrix B.  For example, in my Lesson 4, question 3(a) and 3(d) in the lecture problems right at the start of the lesson have written a system of equations in AX = B form.

 

You will probably find my Practise Problem 31 in Lesson 3 quite helpful with question 5.

 

Question 6 is a Markov Analysis question similar to my question 4 in Lesson 14.  Note: when you are finding the steady-state or stable vector, don't worry about the little tricks I use.  Set up the augmented matrix with a row of ones all the way through the first row, then the rest of the augmented matrix is I - T for the coefficients augmented with a column of zeros.  In other words, do Step 1 as I outline at the start of Lesson 14.  At that point, merely row-reduce the way you always do.  Don't worry about the fancy tricks I show about making zero rows and stuff.  Row-reduce like usual, and the system will solve itself.