Unfortunately, I have decided to no longer offer a seminar for Math 1300, but I am now taking registrations for my exam prep seminars in other courses. Please click this link for more info and to register, if you are interested:
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 2 (Row-Reduction and Linear Systems) to prepare for assignment 3.
Question 1 is just a runthrough of the definitions
for RREF and REF given right at the start of my lesson. Note that none
of the 4 conditions demand that there be leading 1's in an echelon form
matrix. Only if there are nonzero rows must the first
nonzero value be a 1. Also realize that there is no law that says a
leading 1 must be in the top left corner. You are merely required that
each nonzero row begin with a leading 1, and that the leading 1's appear
deeper in the row each time as you go down the rows.
Question 2 is classic Gauss-Jordan elimination like my question 3 in Lesson 2.
Note that question 3 has given you an augmented
matrix, so you may want to draw a vertical line to separate the last
column from the others. This is similar to my question 1 in Lesson 2.
Note that, when they ask how many independent variables are there, they are asking how many parameters are there.
Question 4 is similar to my questions 6, 7 and 8 in Lesson 2.
You should find my question 9 in Lesson 2 quite helpful when you are solving question 5. Feel free to use a calculator on this question if the decimals prove too much for you.
I think you should find my question 12 in Lesson 2 helpful in understanding how to do question 6.
