Even if you are not taking the distance course, I think it is very
useful for all Math 1300 students to attempt these hand-in assignments.
In general, the assignments can be quite demanding and really force you
to solidify your math skills. However, the fact is
that the distance course covers the topics in a different order from the
classroom lecture sections, so I would not advise classroom students to
look at this assignment until after the midterm exam.
Don't have my book? You can download a sample containing two
lessons (Lesson 1 and Lesson 2) here:
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 1 is just classic matrix math stuff. Note, in part (d), you want to isolate CT algebraically first.
Question 2 is a good runthrough of the elementary matrices lesson.
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.
