anonymous
  • anonymous
solve x-y+4z=4, 2x+3y-3z=1, 3x+2y-2z=-1 using matrices
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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jdoe0001
  • jdoe0001
so, I'd think "cramer's rule" in this case works quicker
jdoe0001
  • jdoe0001
so, setup the matrix, and get the Determinant of the 3x3 matrix
jdoe0001
  • jdoe0001
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

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jdoe0001
  • jdoe0001
$$ \left\lbrack \begin{matrix} 1 & -1 & 4 \\ 2 & 3 & -3 \\ 3 & 2 & -1 \\ \end{matrix} \right\rbrack \color{red}{ \begin{matrix} | & 4 \\ | & 1 \\ | & -1 \\ \end{matrix} }\\ D_x = \left\lbrack \begin{matrix} \color{red}{4} & -1 & 4 \\ \color{red}{1} & 3 & -3 \\ \color{red}{-1} & 2 & -1 \\ \end{matrix} \right\rbrack\\ D_y = \left\lbrack \begin{matrix} 1 & \color{red}{4} & 4 \\ 2 & \color{red}{1} & -3 \\ 3 & \color{red}{-1} & -1 \\ \end{matrix} \right\rbrack \\ D_z = \left\lbrack \begin{matrix} 1 & -1 & \color{red}{4} \\ 2 & 3 & \color{red}{1} \\ 3 & 2 & \color{red}{-1} \\ \end{matrix} \right\rbrack\\ \text{and your Determinant for the }\\ \text{denominator will be the Determinant for}\\ D = \left\lbrack \begin{matrix} 1 & -1 & 4 \\ 2 & 3 & -3 \\ 3 & 2 & -1 \\ \end{matrix} \right\rbrack $$
anonymous
  • anonymous
I'm still confused
jdoe0001
  • jdoe0001
ok @Mad_e13
jdoe0001
  • jdoe0001
do you know how to get a determinant?
anonymous
  • anonymous
I don't remember any of matrices because I had the flu when we learned it last year
jdoe0001
  • jdoe0001
well http://easycalculation.com/matrix/learn-matrix-determinant.php and http://www.youtube.com/watch?v=C4yNX4jjHsk let me know any clearing out :)
jdoe0001
  • jdoe0001
@Mad_e13
anonymous
  • anonymous
ok
anonymous
  • anonymous
I understand that. so is that final D the answer or do I keep going?
anonymous
  • anonymous
the 4th post from the top (not counting mine) the very last thing on there ^
jdoe0001
  • jdoe0001
to use Cramer's rule, once you get the Determinants for each variable, then the variable is $$ \cfrac{D_x}{D} = x\\ \cfrac{D_y}{D} = y\\ \cfrac{D_z}{D} = z\\ $$
jdoe0001
  • jdoe0001
it can get tedious, mainly arithmethic really, just gets long, to get the Determinants
jdoe0001
  • jdoe0001
but once you have them, you just put them on top the the Determinant for the 3x3 original matrix
anonymous
  • anonymous
I'm still a little confused but I will ask my teacher about it. thanks for being so patient with me.

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