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.
Week 4
We worked with matrix inverses, seeing how the Gauss-Jordan algorithm can be used to calculate the inverse of a 
Here find a corrected Example 2 from p. 39. In class, I made a slip in the third frame. The row operations are the same.
The final answer is therefore
We also had our second Maple lab.
Week 5
We will see how linear systems can be written as matrix equations, and solved using matrix inverses. Then we will talk about determinants, and perhaps push towards the end of Chapter 1.
Linear Algebra: 20% Test
Will take place Wednesday 14 March, in Week 7.
Maple Catch Up
If you have missed the first lab you have two options: either download Maple onto your own machine (instructions may be found here) or come into CIT at another time to use Maple.
Go through the missed lab on your own, doing all the exercises in Maple. Save the worksheet and email it to me.
Independent Learning
Questions you can do include:
- After Week 4: P. 41, Q. 1-4
- After Week 3: P. 28, Q. 1-5, 6-9 have answers with Q. 7 a harder question. P. 34 exercises.
- After Week 2: P. 18 Q. 2
- After Week 1: P. 18 Q. 1, 3 – 6. Harder questions are 7 and 8. For those who do not yet have the manual, see here.
I am not suggesting you should do all of these. It is recommended by the module descriptor that you do two hours of independent and directed learning every week but of course this isn’t feasible for everyone.
Student Resources
Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc.
J.P. McCarthy: Math Page 
2 comments
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March 6, 2018 at 8:11 am
Student
Hi JP,
I have completed a few of the sample questions. Could you have a look over them to see if they are OK?
March 6, 2018 at 8:14 am
J.P. McCarthy
P.18, Q. 2 (c) “all positive, whole number solutions”. Well you can’t have e.g.
a ten-seater plane: 
must be a whole numbers. Similarly, you can’t have 
15-seater planes: 
must be a non-negative or positive numbers (arguably zero is not positive but I am not too concerned if you include it or not: it is a matter of convention).
P.18, Q. 4 has issues. If you didn’t make a small slip with your row operations, note that every row has a pivot. This implies there is a unique solution and so no parameter.
You have a slight slip when you have
This should be
If you continue from there you should get
, and 
. To Verify your solution by substitution means to substitute these values into the original equation and ensure that these values make the equations true. For example,
P. 18, Q. 5 ii, does have solutions (from where you got to [row two divided by
equivalently row two multiplied by 
]), but there are errors with what you have. Correct solution here:
This implies that
and 
.
P. 18, Q. 5 iii You are good at
To kill the -12 you need to do
. This will leave 
as ![[0\qquad 0\quad|\quad 4]](https://s0.wp.com/latex.php?latex=%5B0%5Cqquad+0%5Cquad%7C%5Cquad+4%5D&bg=ffffff&fg=545454&s=0&c=20201002)
, which implies no solutions.
To check Gaussian Elimination you can download Maple (see here: https://jpmccarthymaths.com/student-resources/) and use the Gaussian Elimination Tutor.
P. 29, Q. 2 (c), you do have a slight issue.
The first row is
: this will become the first column rather than 
so that:
Everything else looks good.
Regards,
J.P.