Math Is Fun Forum

T33N_T1T4N

Member

Registered: 2007-02-10

Posts: 8

sup everybody

name is jonathan, i joined this cuz i love math as much as i like playing my alto sax(which i do like to play a lot). im a sophomore in high school but i learn fast and am fast on solutions within the extenet of my knowledge. i joined mathcounts in middle school and was the ranked 3 within our school. now in high school im really lazy about workin cuz no challenges. i recently found out about how i works like normal numbers, and that kept me entertained for a bit. but what i wanna know and this is the reason i joined, is how matrixs work. like

2x+y+z=4
3x+2y-4z=2
x-y+3z=6

i dunno if thats possible just made up numbers, but i learned to solve it with algebra. but when i asked my teacher how to solve it with a matrix he said he wouldn't tell me cuz u learn it in a higher level math course called linear algebra. i looked it up and found so many different things on it but none i could understand.

so wussup everybody?:D:D

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lets just call it,  i, and get it over with

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: sup everybody

Hi T33N_T1T4N,
Welcome to the forum!
I am sure you'd meet like-minded people here!
Regarding solving the set of simultaneous equations (3 equations in 3 variables) using matrices, you'd first have to learn the multiplication operation on matrices. This you can find here in this forum.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

T33N_T1T4N

Member

Registered: 2007-02-10

Posts: 8

Re: sup everybody

*sretches*
aight gimme an hour or a day to read that through, lots of problems to go thru so it seems explained simple enough

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lets just call it,  i, and get it over with

Mommas Girl

Member

Registered: 2007-01-31

Posts: 68

Re: sup everybody

Hey T33N_T14N, Wassup? Welcome to the Math Is Fun forum, You will have lots of fun on this website.

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"You don't have to like me but you do need to respect me''

soha

Real Member

Registered: 2006-07-07

Posts: 2,530

Re: sup everybody

welcome to the forum T33N_T14N.hope u get the help u need from here

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"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!"
- David O. McKay

WiZaRd

Real Member

Registered: 2006-09-22

Posts: 570

Re: sup everybody

Welcome to the MATHISFUN's Forum

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Be Happy!

Mommas Girl

Member

Registered: 2007-01-31

Posts: 68

Re: sup everybody

Hope you have lots of fun and this website is also good if you need some Homework help

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"You don't have to like me but you do need to respect me''

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: sup everybody

To be honest, I can see why your teacher wouldn't want to explain matrices to you. It would be quite a lengthy explanation, and it's quite possible that you wouldn't have understood most of it. (No offence intended)

Welcome to the forum though, and good on you for researching this independently.
I'll use matrices to solve your system for you, but I warn you: this is kind of jumping in at the deep end, so you'll probably want to look at the link that ganesh posted so that you don't get lost.

2x+y+z=4
3x+2y-4z=2
x-y+3z=6

This system of equations is represented in matrix form like so:

(Sometimes matrices are represtented with normal brackets rather than square ones, but they both represent the same thing)
If we denote the left 3x3 matrix as A, the middle matrix as X and the right matrix as B, then our equation is AX = B.

We want to find X, and so we need to get rid of the A in that equation. To do this, we need to premultiply both sides by A[sup]-1[/sup]. By definition, A[sup]-1[/sup]A = I (The identity matrix) and so we will be left with just X on that side. That would work with postmultiplying as well, but if we did that then the operation on the right-hand side wouldn't be defined.

To find the inverse of A, we need to find its determinant and its adjugate.
First, the determinant:

                           

To find the adjugate of A, we first find its matrix of minors:

Then its matrix of cofactors:

And then the transpose of this is the adjugate:

Divide the adjugate by the determinant, and we have the inverse:

Premultiplying both sides of our original matrix equation by this gives the following:

Now all we need to do is perform the matrix multiplication on the right-hand side:

And there, finally, we have it.
Your solution is x = 18/7, y = -12/7, z = 4/7.

Checking against the three original equations will verify that this works. Of course, just solving them the 'normal' way may well have been quicker.

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Why did the vector cross the road?
It wanted to be normal.

lightning

Real Member

Registered: 2007-02-26

Posts: 2,060

Re: sup everybody

i love the teen titians i like raven the best then beastboy then starfire then cyborg then robin

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