challenge for Nicole

[Jonathan Joo]

ok, here's my question for Nicole:

what is the determinant of 

 3 -3

-5 2

times the determinant of

9  2

1 -2

?

-Jonathan

[James Crook]

Jonathan,

Probably best to say:

"Show that the rule for product of determinants holds for these two matrices."

That way Nicole would have to write out a matrix multiplication as well.

With the question you asked, she could just calculate and tell you the values of some determinants.

--James.

[Nicole Shih]

6+5=(21)*-18-2=(20)=420,

det([a  b])= ad-bc 

      [c  d]

[James Crook]

Nicole,

You wrote '5' when you meant '15' in the first line, and that had me confused.

The way you have written your answer is a bit confusing too, so I would write it like this:

For the first matrix:

a=3,b=-3,c=-5,d=2

The determinant is:

(a*d) - (b*c)

So that's:

(3*2) - (-3*-5) = 6 - 15 = -9

Writing it out in full makes it a lot easier to see where you went wrong on the sign.  You ended up adding 6 and 15.

For the second matrix:

a=9,b=2,c=1,d=-2

The determinant is:

(a*d) - (b*c)

So that's:

(9*-2) - (2 * 1) = -18 - 2 = -20

So again you got the sign wrong.  It's very easy to get the sign wrong, it just takes time and practice, and often you have to write out more than you would really like to to make sure you get it right.  

Anyway,  calling the first matrix A and the second matrix B

we have:

det( A ) = -9

and

det( B ) = -20

I would like to see that you can multiply 2x2 matrices.  That's part of the challenge too.

Can you write out the multiplication for A times B that gives a new 2x2 matrix C?

I would like you to then calculate the determinant of that matrix C writing out the details in full like I have.

We hope the determinant of that matrix will be -9 * -20 = 180, because otherwise the rule about determinants is wrong.

--James.

[Nicole Shih]

For the first matrix:

a=6, b= 2, c=8, d=3

 

The determinant is

(a*d)-(b*c)

 

So that's:

18-16=-2

 

For the second matrix:

a=2, b=4, b=15, d=-6

The determinant is (a*d)-(b*c)

 

So that's:

-12-60=-72

 

Det (A)=-2

 

Det(B)=-72

-72*-2=144

[James Crook]

I've put a page on the wiki on matrix multiplication that may be helpful to the group.

http://onlinemathcircle.com/wiki/index.php?title=Example:_Matrix_Multiplication

I'm thinking that matrices are not taught well in the States at high school level.  We're going to have to find a way to fix this.  Matrices are a vital mathematical tool used in mathematics, engineering and computing.  Once you get used to what they can do you wouldn't want to do without them.

--James.

On 24 June 2011 18:11, Jonathan Joo <jonath...@yahoo.com> wrote:

[Nicole Shih]

[6  2]* [2   4]    

[8  3]  [15 -6]

=[12+30  24-12] 

  [16+45  24-18]

=[42  12]

  [61  6]

[Nicole Shih]

no, well my earlier post was because I thought you wanted me to make my own A and B and then do it.

[James Crook]

Jonathan,

If this is correct and you are happy Nicole knows the requested techniques for matrices, please tell Shri so he can tick the box and we can get this group task completed.

Shri, how about an update to the list.  Who are we waiting for?

--James.

[Jonathan Joo]

Hi,

Sorry for the late response, I just found this email among my cluttered inbox. Yes, this is fine, so Shri can tick the box off. 

Thanks!

-Jonathan

---

From: James Crook <james....@gmail.com>
To: l2lea...@googlegroups.com
Sent: Sunday, June 26, 2011 5:58 AM
Subject: Re: challenge for Nicole