Maths Help - Gaussian Elimination

[tntcoder]

Hi,

Hoping someone can help me with this as I have no idea what im doing

Say I have 3 equations in this format:

I got these from doing Lagrange Interpolation on some points, and I now need to form a polynomial out of these equations, specifically I am interested in the first coefficient of the resulting polynomial.

I don't know how to solve this system of equations though, but I think I need to use Gaussian Elimination, which involves moving the equations to matrix form (Vandermonde matrix?).

I think this is the correct matrix:

Could anyone explain in simple terms how it's solved? EDIT: this is also in GF(17) so everything is mod 17.

Thanks a lot.

 

[inflynx]

(1 1 1 | 30 )
(1 2 4 | 61 )
(1 4 16 | 159)
--------------
(1 1 1 | 30 )
(0 1 3 | 31 )
(1 3 15 | 129)
--------------
(1 0 -2 | -1 )
(0 1 3 | 31 )
(0 3 15 | 129)
--------------
(1 0 -2 | -1 )
(0 1 3 | 31 )
(0 0 6 | 36)
--------------
(1 0 -2 | -1 )
(0 1 3 | 31 )
(0 0 1 | 6)
--------------
(1 0 -2 | -1 )
(0 1 0 | 13 )
(0 0 1 | 6)
--------------
(1 0 0 | 11 )
(0 1 0 | 13 )
(0 0 1 | 6 )
--------------
==> a0=11; a2=13; a3=6

read wikipedia page on Gaussian Elimination to see what is done

 

[Gothic Draconia]

Edit: I know what i am doing and thought that i would share it with all.

 

[killari]

I got the same answer as inflynx using the matrix inverse method for solving a system of equations, so you can always try that as well.

 

[tntcoder]

I got the same answer as inflynx using the matrix inverse method for solving a system of equations, so you can always try that as well.

Thanks guys, will give that method try. I just about understand inflynx's working, but the wiki doesn't explain it too well.

 

[shmacks]

Nice to know that some people can do still do decent maths compared to the appauling questions people sometimes ask on here. What was someone asking the other day; what 3-2+5 is equal to or something. grrrr

 

[dante6491]

You can stop after the 4th matrix since any further and that becomes complete elimination. For Gaussian you get the value of a3 or Y or whatever it is called then substitute upwards.

On an unrelated note where about's in London are you? I was studying this last week the week before at uni.

 

[tntcoder]

You can stop after the 4th matrix since any further and that becomes complete elimination. For Gaussian you get the value of a3 or Y or whatever it is called then substitute upwards.

On an unrelated note where about's in London are you? I was studying this last week the week before at uni.

Thanks, after hundreds of sheets of paper think I finally understand the method now I'm near old street, studying at ucl but this is for part of my thesis as I would otherwise avoid maths at all costs

 

[Andy100]

Nice to know that some people can do still do decent maths compared to the appauling questions people sometimes ask on here. What was someone asking the other day; what 3-2+5 is equal to or something. grrrr

Not quite, I was asking how someone had managed to get an answer other than 7 to 3-1+5.

 

[inflynx]

studying at ucl

I graduated from UCL. What department are you at?