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.


Please bring E10.50 with you next week for your manual if you haven’t done so already. Those of you who didn’t get one last week will next week.

Week 2

We looked at the solution space of linear systems.

Week 3

We will introduce matrices as linear maps. In Maple, we will learn how Maple handles linear systems with no and infinite solutions. We will also use the Maple Tutor to help us do the below exercises.

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 — on P.20 — at this point include (Q.2 should not be there):

  • Q. 1
  • Q. 4
  • Q. 5-7
  • Q. 8
  • Q. 9

Question 3

From P.20… we start by putting the system into augmented matrix form:

\left[\begin{array}{ c c c | c } 1 & 1 & -1 & 1 \\ 1 & 2 & -2 & 0 \\ -2 & 1 & 1 & 1 \end{array}\right]

r_2\rightarrow r_2-r_1,\,r_3+2r_1,

\displaystyle \left[\begin{array}{ c c c | c} 1 & 1 & -1 & 1 \\ 0 & 1 & -1 & -1 \\ 0 & 3 & -1 & 3 \end{array}\right]

r_3\rightarrow r_3-3r_2,

\displaystyle \left[\begin{array}{ c c c | c} 1 & 1 & -1 & 1 \\ 0 & 1 & -1 & -1 \\ 0 & 0 & 2 & 6 \end{array}\right]

r_3\rightarrow \frac12 \cdot r_3,

\displaystyle \left[\begin{array}{ c c c | c} 1 & 1 & -1 & 1 \\ 0 & 1 & -1 & -1 \\ 0 & 0 & 1 & 3 \end{array}\right]

r_2\rightarrow r_2+r_3,\,r_1\rightarrow r_1+r_3,

\displaystyle \left[\begin{array}{ c c c | c} 1 & 0 & 0 & 2 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 3 \end{array}\right]

r_1\rightarrow r_1-r_1,

\displaystyle \left[\begin{array}{ c c c | c} 1 & 1 & 0 & 4 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 3 \end{array}\right]

\Rightarrow z=3,\,y=2\text{ and }x=2.

Maple Online & Wolfram Alpha

I am aware that some of us have not been able to install Maple… I have got to here:

Maple Download

If  you cannot get to this screen please email me and I might be able to help (sadly I don’t have admin rights on the computer I am working on right now so cannot find out do I need the 32 bit or the 64 bit…).

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.

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


Provisionally I am looking at Week 7. Ye will get a sample test (format only) and notice two weeks in advance.

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 the solution set of a linear system.

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.