Below are the worksheets for the tutorials for MH2814.

**Tutorial 2**

Worksheet with blanks.

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Below are the worksheets for the tutorials for MH2814.

**Tutorial 2**

Worksheet with blanks.

Some FAQs (updated now and then).

**I’ve excluded the Chapters 17 to 20 from David Lerner’s notes. Does that mean that orthogonal projections, inner product and trace will not be tested?**

No. I excluded them because in the notes, more “advanced” concepts are discussed in the chapters. For example, the chapter on inner product introduce the concept of positive definite and bilinear, which may be confusing. However, you will still need to know that how to compute the inner product between two vectors and what it means for two vectors to be orthogonal.

Similarly, orthogonal projection and trace are classic examples of linear transformations. Hence, you should be able to determine the kernel and range of these transformations. For example, Tut 10 Q2 asks you to determine the range of a trace map, which is within your ability. However, we will not ask you to show that trace map is invariant with respect to a change of basis.

**I do not understand the concept of determining a matrix associated with a linear transformation.**

Please take a look at this video from khan academy. I hope this is more illuminative.

**Tut 11, Q4 is wrong.**

My apologies. I’ve updated the worksheet.

**When am I going to provide the feedback for the Final Sample?**

Now. Here are the solutions with some feedback. Do not be too bothered by question 5.

If you want to find out more about projections as linear transformation, you can look at this video.

**Am I going to provide the answers for the tutorial fill-in the blanks?**

Here are some general guidance to studying linear algebra:

David Lerner’s notes are useful for self-study. They contain small exercises that help understanding and sometimes give hints to the tutorial questions.

Chapters to take note are: Ch 1- 8, Ch 10-13, Ch 15.

Khan Academy also has a comprehensive course for linear algebra too.

Relevant videos/lessons are:

It looks a lot, but the videos are typically very short. You can also select the topics to revise.

For those who prefer the “abstract” flavour, you can search for the text Linear Algebra Done Right by Sheldon Axler. (The link is the link to the official website. The book is easily found online, but I would not place it here.) This text is probably more useful for Linear Algebra 2.

My consultation hours are: Mon – Wed, 10am to 5pm. Please drop an email to arrange for consultation.

Good luck for your examinations!

Here is some feedback for those who submitted the midterm samples.

There are some who attempted Q5 to Q7 (in Tutorial 6). I have also provided the solutions and feedback for these questions too.

**Question 1 and 5**

**Solution**: (Q1) Since the equation contains the term , there are no values of that make the equation linear. (Q5) Since the equation contains the term , there are no values of that makes the equation.

**Feedback**: Unless otherwise specified, unknowns in an equation are given by , and . For an equation to be linear, any term containing an unknown must be of the form (constant)(unknown). Terms like and are not of the required form and hence, the equation is not linear.

Some mistakes:

- Writing “” and “” to mean “there are no values of ”. This is not the case. “” means can be . “” means is a set which contains no element.
- There is a solution that states , because is in fact two straight lines. This is
**not**correct. Prof Putinar mentioned that is in some sense “linear”. Do**not**interpret this as saying that the equation is linear. By definition, both and are not linear equations.

Reposted from SPMS Student Welfare:

Hi Year 1s! We would like to have your feedback and suggestions on SPMS Freshmen Orientation 2013. Please click here to access the survey! Appreciate the time taken! Thank you!

**Fill-in-the-blanks Tutorial Solutions**

Tutorial 8

Tutorial 9

Tutorial 10

Tutorial 11

**Mini Revision Quiz 2**

Slides

**Tutorial 11**

Worksheet with blanks.

Quiz 3 solutions and feedback.

**Tutorial 10**

Worksheet with blanks.

Worksheet with solutions.

**Tutorial 9**

Worksheet with blanks.

Worksheet with solutions.

**Tutorial 7**

Worksheet with blanks.

Worksheet with solutions.

**Mini Revision Quiz**

Slides

Quiz 2 was well done. Everyone got full credit for this quiz.

**Tutorial 5**

Worksheet with blanks.

Worksheet with solutions.

**Tutorial 4**

Worksheet with blanks.

Worksheet with solutions.

**Tutorial 3**

Worksheet with blanks.

Worksheet with solutions.

Quiz 1 was generally well done. Almost everyone got full credit for this quiz.

**Tutorial 2**

Worksheet with blanks.

Worksheet with solutions.

**Tutorial 1**

Worksheet with blanks.

Worksheet with solutions.

Do note that I would be overseas from 26 Apr (Fri). Hence, I would *not be available for consultation nor be able to answer an queries (including emails)*.

Good Luck for the Examinations!

For students taking MH3100/MTH311, I sincerely like to seek your feedback on the the conduct of the tutorials.

Please access this link to provide your feedback. Feel free to make ANY comments and your feedback will be taken seriously and taken into consideration (if I ever get to teach again).

Note that the link is only available until 21 Apr (Sun).

Regards,

HanMao