Math 1310: Tips for Assignment 4

Published: Tue, 03/03/15

Have you tried my Audio Lectures?
Especially since I no longer offer seminars in this course, you really should consider getting my Audio Lectures.  They really do help.

You can download a free sample of my book and audio lectures containing Lessons 1, 2 and  3:
Did you read my tips on how to study and learn Math 1310?  If not, here is a link to those important suggestions:
Did you see my tips for Assignment 1? Click here
Did you see my tips for Assignment 2? Click here
Did you see my tips for Assignment 3? Click here
Tips for Assignment 4
Here is a link to the actual assignment, in case you don't have it handy:
Study Lesson 10 (Determinants and Their Properties), Lesson 11 (Adjoint Matrices), Lesson 12 (Cramer's Rule), and Lesson 13 (Markov Analysis) from my Matrices for Management book to prepare for this assignment.
PLEASE NOTE:  I have totally re-jigged my Matrices for Management book this year.  Two new lessons have been added, and I have changed the order of many of the other lessons to better fit the syllabus for the distance course.  I always appreciate it when students purchase the current edition of my books, as that does subsidize my efforts to offer things like these free tips.  If you choose to make do with an older edition of my book, please realize that you are missing some things, but you can probably make do.  I leave it up to you to look at the Table of Contents in my free sample of the book above to clarify what lesson number in your old book pertains to the lessons I mention in my tips.
Question 1
A good runthrough of Determinant Properties as taught in Lesson 10 of my book.  Also make sure you have done the Adjoint lesson (Lesson 11) before you do this question.  Question 2 in Lesson 10 and Question 3 in Lesson 11 are especially helpful.
Question 2
This is a Markov Analysis question similar to my question 4 in Lesson 13

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 13.  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.  I really regret over-complicating this lesson by giving too many tricks when it is ultimately just a row-reduction problem. 

DO NOT USE THE CRAMER'S RULE METHOD I DEMONSTRATE!  Stick to good old row-reduction.
Question 3
Very similar to my Lesson 10, question 5.
Question 4
Very similar to my Lesson 10, question 6.
Question 5
Very similar to my Lesson 11, question 1.  Obviously, in part (e), they want you to solve X.
Question 6
Very similar to my Lesson 12, question 1.