**I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.**

## Test

Due to the lost night in the storm, I am now putting the test in Week 8. Ye will get a sample test (format *only*) in week 6. It will be on Chapter 1.

## Maple Catch Up

If you want to do Maple catch up, if for example you miss a lab, please download the Maple file from your email, do the exercises in Maple (either in a new worksheet or on top of the original file with the exercises), save the worksheet and email me the worksheet you were working on.

## Week 5

We found some matrix inverses using the Gauss-Jordan Algorithm and saw how matrix inverses are useful in solving matrix equations. In particular, we saw that we can rewrite a linear system as a matrix equation. In Maple, we saw how Maple handles linear systems with no and infinite solutions. We also used the Maple Tutor to help us do some matrix manipulations.

## Week 6

We will solve a number of linear systems using this inverse matrix method. Note however that this cannot work if the solution is not unique… we will use a property of matrices called the determinant to decide in advance if a certain class of linear system, homogenous systems, have a unique solution or not. If the matrix (of coefficient) is invertible then the solution has to be unique and we will see that the matrix (of coefficients) is invertible if and only if the determinant is non-zero. Finally we will look at Cramer’s Rule: a method for solving for only *one *of the variables of a linear system.

## Independent Learning: Exerices

You are supposed to be working outside of class and I am supposed to help you with this. Working outside of class means doing the exercises in the notes. Any work that is handed up will be corrected by me. Also you can ask me a question here on this site and I will answer it ASAP.

Questions that you can do at this point include:

- p.44 exercises
- p.46 exercises
- p. 52 Q. 1, 3(i),(ii) & 4

### Maple Online & Wolfram Alpha

If you are subscribed to CIT MathsOnline you will have free access to the mathematical software package *Maple:*

**Self-enrolment for Maths Online**

1. Log into Blackboard Learn

2. Click on the Courses tab button at the top of the screen. Go to Course Search and type Maths Online in the box.

3. Once you’ve found the course, click the non-credit-course button and click on Enrol. This should take you to the Self Enrolment page.

4. Your Access Code is mathsonline (lower case, no spaces).

5. After you’ve finished click Submit. You should now see a message that says your enrolment was successful.

Once you’ve enrolled, no go back to the Blackboard home page and click on the Maths Online button: it should be under an Academic Learning Support Tab. You can download Maple by selecting the *Mathematical Software* tab in the left hand column and following the instructions under the Maple item. Click Maple text to start.

If you have any problem with this take a print screen and send it to me and I will try and sort you out.

I myself am not a *Maple *expert but ‘grew up’ with another mathematical software package *Mathematica*. *Mathematica *powers the “computational knowledge engine” WolframAlpha. Go on ask it a question!

## Academic Learning Centre

Those in danger of failing need to use the Academic Learning Centre. As you can see from the timetable there is evening support. You will get best results if you come to the helpers there with *specific *questions.

## Math.Stack Exchange

If you find yourself stuck and for some reason feel unable to ask me the question you could do worse than go to the excellent site math.stackexchange.com. If you are nice and polite, and show due deference to these principles you will find that your questions are answered promptly. For example this question about matrix inverses.

## Additional Notes: E-Books

If you look in the module descriptor, you will see there is some suggested reading. Of course I think my notes are perfect but if you can look here, search for ‘Bird Higher Engineering’ you will see that the library have an E-Book resource.

## 2 comments

Comments feed for this article

March 4, 2014 at 8:02 pm

Student 51Hi JP,

I was just having a look at those questions that you recommended to look at. Just on question 4 on page 52, what exactly does it mean when it says prove the solution is unique?

March 4, 2014 at 8:08 pm

J.P. McCarthyHi,

Show that there is only one solution, not an infinite number of solutions and not no solution.

Recall that a linear system can have a unique solution, an infinite number of solutions, or no solutions.

To show that the solution is unique whenever exists just multiply both sides of on the left by .

Recall that is what we are looking for and is some (known) vector of constants.

I wouldn’t be too worried about this question either way, it is just an exercise testing you on the theory.

Regards,

J.P.