Maths, algorithms and the Euclidean Algorithm!

[Pace]

Following on from Paddy's quest for assistance, I offer something less 'biological'

So, um, can anyone answer these?

1. Let a and b be integers and m be a positive integer. Show that a = b (mod m) if and only if a mod m = b mod m.

2. Using the Euclidean Algorithm, find gcd(1529,14038). Show your working.

3. Find an inverse of 2 modulo 17. Use your answer to solve the linear congruence 2x = 7 (mod 17). Show your working in each case.

4. (a) The n x n matrix A is called a diagonal matrix is a`ij=0 for i/=j. Show that the product of two diagonal matrices is again a diagonal matrix. Simplify the algorithm for computing the product of two n x n matrices A and B for the special case that each of A and B is an n x n diagonal matrix.

(b) The n x n matrix A is called an upper triangular matrix if a`ij=0 for i>j. Show that the product of two n x n upper triangular matrix is again an upper triangular matrix. Simlpify the algorithm for computing the product of two n x n matrices A and B for the special case that each of A and B is an n x n upper triangular matrix.

Um, that will do for now I've got the answer to 2 I believe, and I'm working in 4 at the moment (coz I'm good with a matrox, er matrix! )

TIA,

Paul.

Ans 2:
gcd(1529,14038)
14038 = 1529 · 9 + 277
1529 = 277 · 5 + 144
277 = 144 · 1 + 133
144 = 133 · 1 + 11

gcd is therefore 1?

[Jorden]

Time for the Men in White, Paul?

Now, for an answer... errm...

[i]If you take the Alfa of the tan(45)x Gamma of Cos(3), your answer will be somewhere around there

I hope it was fun for you to type over your book

Jord.

[Paddy]

I don't know much (er.. anything really!) about maths, but I am learning a lot about stools....so I hope this helps.

...it sure looks comfy!

[Pace]

Um, do those stools come in a set? If so, I might buy a couple of them, but I can't differentiate between them

Also, when will we be seeing the famous wink replacing the ubb one?

Paul.

[Pace]

And I've just noticed that I didn't finish question 2 above - so here's what I got (I cannot believe how crap I am at this!)

gcd(1529,14038)
14038 = 1529 · 9 + 277
1529 = 277 · 5 + 144
277 = 144 · 1 + 133
144 = 133 · 1 + 11
133 = 11 · 12 + 1
11 = 11 · 1 + 0

Therefore we get a GCD (greatest common divisor) of 1.

Who offered help to this before? I asked a previous question and someone knew something about this! I need anything...(except question 2 )

Cheers,

Paul.

[Pace]

Up

And an update: I've done Q4 fairly well...

So, um, any help with Qn's 1 & 3?

(Paul, ever so desperate now... )

[CHHAS]

Pace, I wrote a paper on that in Highschool, the knowledge is lotsa booze behind me, but I just might have the paper somewhere

I'll look for it when I get home.

[Pace]

Um, thanks for the offer CHHAS, but I need to hand this in within the hour now. I've done as much as I can...

Paul.