urgent matrices help

[anonymous1]

how do i solve the following using matrices:
2x - 3y + z = 3
-3x + y - 2z =1
x- y - z = 6

thanks

[ligands]

Put 2 -3 1, -3 1 -2, 1 -1 -1 in 3x3 matrix call this A
Put x,y,z in a colum matrix this X
Put 3, 1, 6 in a colum matrix this B

To find x y z set up the equation X = A^-1B

[anonymous1]

so B * A^-1

[ligands]

Yep sorry if it's messy on phone lol, the original equation will be AX = B and to find X you need to go A^-1AX = A^-1B which equals IX = A^-1B which means X = A^-1B and A will be the coefinet matrix, x will be the variable matrix and b will be the answer matrix, I think I put it the wrong way around in the other comment let me edit it

[Flying Emu]

This what you mean lig?

--             --      -- --        -- --
|  2  -3   1 |      | X |        | 3 |
| -3  1   -2 |  X  | Y |   =   | 1 |
|  1  -1  -1 |      | Z |        | 6 |
--             --      -- --         -- --

*Yes i know, horrible brackets.

[Phy124]

This what you mean lig?

--             --      -- --        -- --
|  2  -3   1 |      | X |        | 3 |
| -3  1   -2 |  X  | Y |   =   | 1 |
|  1  -1  -1 |      | Z |        | 6 |
--             --      -- --         -- --

*Yes i know, horrible brackets.

Heh, nice work (Easier method below)

Code: [Select]

[tex]\begin{bmatrix}
2 & -3 & 1\\
-3 & 1 & -2\\
1 & -1 & -1
\end{bmatrix}\begin{bmatrix}
x\\
y\\
z
\end{bmatrix}=\begin{bmatrix}
3\\
1\\
6
\end{bmatrix}[/tex]
Use this for help







Solve for X;



By the way, I realise I'm just reiterating what has previously been discussed, just showing you guys some latex code in the progress. (Time to try and get everyone on these boards on latex I reckon )

edit:

I forgot to mention you can also solve it using the solve function on your calculator.

(From what I remember regarding TI-89) The calculator has a solve function for two unknowns, you can just add a third equation to this and a third unknown to solve for. This might be quicker then putting all those values into a matrix.

IIRC it was something like;

Solve(  and    for {a,b})

and you could just change it to;

Solve(2x-3y+z=3 and -3x+y-2z=1 and x-y-z=6 for {x,y,z})

[ligands]

haha yer i was on my phone so i couldn't be bothered using latex

[anonymous1]

thanks everyone

[Flying Emu]

Heh, nice work (Easier method below)

OH WOW.... T.T