Math 1310: ICYMI Tips for Assignment 3

Published: Sat, 02/21/15

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?
Did you see my tips for Assignment 2?
Tips for Assignment 3
Here is a link to the actual assignment, in case you don't have it handy:
You need to study Lesson 6 (Matrix Math), Lesson 7 (The Inverse of a Matrix and Applications) and Lesson 8 (Leontief Models) 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 Matrix Math problems as taught in Lesson 6 of my book.  Note, by I2 and I3, they mean the 2 by 2 and 3 by 3 Identity matrices, respectively.
Question 2
More Lesson 6 and 7 stuff.  You are going to need to compute an inverse in this problem, but isolate S in the equation first.  Note that, the first step should be to factor S out on the left side.  But what is left behind in that second term after you pull S out?  Be sure to read through Lesson 6 carefully.
Question 3
Very similar to my question 1 in Lesson 7.
Question 4
A Leontief Open Model question as taught in Lesson 8 of my book.
Question 5
A Leontief Closed Model question as taught in Lesson 8 of my book.  Please disregard my trick to quickly create a zero row in these matrices.  It is an unnecessary complication.  Once you have set up your matrix, just proceed to row-reduce the way you know how and the zero stuff will take care of itself.

If you have set up your matrix correctly, remember each column must total up to exactly 1.  Your matrix will be full of fractions, (halves, quarters, fifths, and tenths).

Once you set up the appropriate augmented matrix, I suggest you get rid of the fractions first by multiplying each row by the common denominator for that row.

Note that there are always infinite solutions to these problems.  Assuming a parameter, t, shows up in your solution, a fair way is to make that value t dollars.  Then you can list the value of each industry in terms of t.