Question

solve x-y+4z=4, 2x+3y-3z=1, 3x+2y-2z=-1 using matrices

Answer 1

so, I'd think "cramer's rule" in this case works quicker

Answer 2

so, setup the matrix, and get the Determinant of the 3x3 matrix

Answer 3

http://i1.ytimg.com/vi/PO4hpSyxH9g/mqdefault.jpg

those there are the Determinants for each variable, the one in the picture is a 2x2
but the procedure is the same for a 3x3 or else
the only thing for a 3x3 the Determinant is nested one level further below

Answer 4

$$
\left\lbrack
\begin{matrix}
1 & -1 & 4 \\
2 & 3 & -3 \\
3 & 2 & -1 \\
\end{matrix}
\right\rbrack

\color{red}{
\begin{matrix}
| & 4 \\
| & 1 \\
| & -1 \\
\end{matrix}
}\\
D_x = \left\lbrack
\begin{matrix}
\color{red}{4} & -1 & 4 \\
\color{red}{1} & 3 & -3 \\
\color{red}{-1} & 2 & -1 \\
\end{matrix}
\right\rbrack\\

D_y = \left\lbrack
\begin{matrix}
1 & \color{red}{4} & 4 \\
2 & \color{red}{1} & -3 \\
3 & \color{red}{-1} & -1 \\
\end{matrix}
\right\rbrack
\\
D_z = \left\lbrack
\begin{matrix}
1 & -1 & \color{red}{4} \\
2 & 3 & \color{red}{1} \\
3 & 2 & \color{red}{-1} \\
\end{matrix}
\right\rbrack\\

\text{and your Determinant for the }\\
\text{denominator will be the Determinant for}\\
D = \left\lbrack
\begin{matrix}
1 & -1 & 4 \\
2 & 3 & -3 \\
3 & 2 & -1 \\
\end{matrix}
\right\rbrack
$$

Answer 5

I'm still confused

Answer 6

ok @Mad_e13

Answer 7

do you know how to get a determinant?

Answer 8

I don't remember any of matrices because I had the flu when we learned it last year

Answer 9

well
http://easycalculation.com/matrix/learn-matrix-determinant.php
and
http://www.youtube.com/watch?v=C4yNX4jjHsk
let me know any clearing out :)

Answer 10

@Mad_e13

Answer 11

ok

Answer 12

I understand that. so is that final D the answer or do I keep going?

Answer 13

the 4th post from the top (not counting mine) the very last thing on there ^

Answer 14

to use Cramer's rule, once you get the Determinants for each variable, then the variable is

$$
\cfrac{D_x}{D} = x\\
\cfrac{D_y}{D} = y\\
\cfrac{D_z}{D} = z\\
$$

Answer 15

it can get tedious, mainly arithmethic really, just gets long, to get the Determinants

Answer 16

but once you have them, you just put them on top the the Determinant for the 3x3 original matrix

Answer 17

I'm still a little confused but I will ask my teacher about it. thanks for being so patient with me.