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Don't have my book or audio? You can download a free sample of my book and audio lectures containing Lessons 1 and 2: Did you read my tips on how to study and learn this course? If not, here is a link to those important suggestions: Here is a link to the actual assignment, for those of you who don't have it: Study Lesson 1: Systems of Linear Equations and Lesson 2: Row-Reduction and Linear Systems in my book, if you have it, to prepare for this assignment.
Of course, always seek
out assistance from my book, your course notes, etc. if you ever hit a question you don't understand, but try not to be learning things as you do an assignment. Learn first, then put your learning to the test.
This question is too easy! Strangely, they don't want you to solve anything. Just express the system as an augmented matrix. Basically that is the first step in preparing to row-reduce as taught in Lesson 2 of my book. But don't do any
row-reduction! Just write the augmented matrix and quit.
I define a RREF and REF matrix in the first couple of pages of Lesson 2. Note that, if a matrix is RREF it must certainly also be REF (in other words, it is both), but a matrix can be REF and not RREF. My Lesson 2, #11 might also help you
clarify the definitions.
The wording in this question is confusing. It seems to suggest they want you to attempt to solve it using the methods I teach in Lesson 1, but they ask you to make an augmented matrix, which suggests that they actually want you to row-reduce the system as taught
in Lesson 2. You may want to ask the prof if they want you to use row-reduction here. I think that is the best approach.
Look at my Lesson 2, #6-8 for examples of the kind of problem we are dealing with here. Your matrix is going to have a and b in it.
You could also solve this by elimination and substitution like I show in Lesson 1, but you have to be careful.
Look at the x and y terms in both equations you are given.
- As I discuss in Lesson 1, a linear system with two variables has no solution when two lines are parallel. Two lines are parallel if they have the exact same x terms in both equations (which they do here), the exact same y terms in both equations (what would a have to be for the two y terms to be identical?), but the equations equal different values (what would b have to be to make it
different from the other equation?).
- A linear system with two variables has infinite solutions when two lines are identical (one line graphs directly over top of the other line). Two lines are identical if they have the exact same x terms in both equations (which they do here), the exact same y terms in both equations (what would a have to be for the two y terms to be identical?), and the equations equal the exact same values (what would b have to be to make
it exactly the same as the other equation?).
- Otherwise, two lines will intersect at exactly one point (one solution). Here, that will happen provided a is not the value that makes the y terms identical. So, for all other values of a solve the system by elimination as taught in Lesson 1. You are answer for x and y will be a mess, including a and b all over the place.
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