how to inverse 3x3 matrices

hello guys!!
really need your help rite now..i;m having problem on how to inverse 3x3 matrix using php.
hope guys out there who had better info bout this can help me..:(

Is that mathematical inversion of the matrix or just interchanging rows and columns?

Is that mathematical inversion of the matrix or just interchanging rows and columns?

emm..it is the mathematical inversion of the matrix...its really make me mad..:(
guide me please...

Tell me the mathematical way how to do that (or give link to a matrix tutorial). Its been long I studied them, and I have forgotten the way to invert it.

And show me if you tried something, I'll help you further..

[PHP]<?php

//SIZE OF SQUARE MATRIX (CAN BE ANY DEPENDING UPON solve_matrix($m) FUNCTION)
$size = 3;
if (!isset($_POST['submit']))
{
echo "<form action=\"".$_SERVER['PHP_SELF']."\" method=\"post\"><center><br><br><h2>Calculate ".$size."x".$size." Matrix Inverse</h2><br>";
for ($i=0; $i<$size; $i++)
for ($j=0; $j<$size; $j++)
{
echo "<input type=\"text\" name=\"x_".$i."_".$j."\" style=\"width:50px;text-align:center;\">";
if ($j==$size-1) echo "<br>";
}
echo "<br><input name=\"submit\" type=\"submit\" value=\"Calculate Inverse\"></center></form>";

}

else
{

for ($i=0; $i<$size; $i++)
for ($j=0; $j<$size; $j++)
if (filter_var($_POST['x_'.$i.'_'.$j], FILTER_VALIDATE_INT)===false)
die ('<br><center><h3>Invalid Data Type</h3></center>');

echo "<center>";

$matrix = array();
for ($i=0; $i<$size; $i++)
for ($j=0; $j<$size; $j++)
$matrix[$i][$j] = $_POST['x_'.$i.'_'.$j];
unset($_POST);

display_matrix($matrix, "<b>Matrix</b>");

$I_matrix_I = solve_matrix($matrix);
if ($I_matrix_I==0) die('NULL MATRIX');

$adjoint = array();
$inverse = array();
for ($i=0; $i<$size; $i++)
for ($j=0; $j<$size; $j++)
{
$cofactor = array();
for ($k=0; $k<$size; $k++)
{
if ($i!=$k)
{
$temp = array();
for ($l=0; $l<$size; $l++)
{
if ($j!=$l)
array_push($temp, $matrix[$k][$l]);
}
array_push($cofactor, $temp);
}
}
display_matrix($cofactor, "<b>Cofactor</b> _{".($i+1).($j+1)."}");
$adjoint[$j][$i] = solve_matrix($cofactor)*pow((-1),($i+$j)); //INTERCHANGING $i $j RESULTS TRANPOSE
}
display_matrix($adjoint, "<b>Adjoint</b>");

for ($i=0; $i<$size; $i++)
for ($j=0; $j<$size; $j++)
$inverse[$i][$j] = $adjoint[$i][$j]/$I_matrix_I;

display_matrix($inverse, "<b>Inverse</b>");
}

//WORKS ONLY FOR UPTO 3x3
function solve_matrix($m)
{
$_size = count($m);
switch ($_size)
{
case 1:
return $m[0][0];
case 2:
return (($m[0][0] * $m[1][1]) - ($m[0][1] * $m[1][0]));
case 3:
return ($m[0][0]*($m[1][1]*$m[2][2]-$m[1][2]*$m[2][1])) - ($m[0][1]*($m[1][0]*$m[2][2]-$m[2][0]*$m[1][2])) + ($m[0][2]*($m[1][0]*$m[2][1]-$m[2][0]*$m[1][1]));

//CAN BE INCREASED TO ANY NUMBER
//YOU CAN MAKE A BETTER FUNCTION WITH FOR LOOP WHICH COULD GO TO ANY LIMIT
//USE THE ABOVE COFACTOR LOGIC FOR THAT
default:
return 0;
}
}

//DISPLAY A MATRIX IN A TABLE
function display_matrix($m, $name)
{
echo $name."<br><table border=\"1px\" cellpadding=\"2px\" style=\"border-collapse:collapse;\">";
foreach($m as $row)
{
echo "<tr>";
foreach ($row as $value)
{
echo "<td>".$value."</td>";
}
echo "</tr>";
}
echo "</table>
<br>";
}
?>[/PHP]

See how's this... ;)

Regards,
Harpreet

dear Harpreet..
tenkiu so much for giving me that..:)
but i cant run it when i combine ur program with mine...
emm...can u help me futhermore??
this is the link for invertible matrix eqn...http://en.wikipedia.org/wiki/Invertible_matrix

and below is part of my program that needs me to inverse it.. really hope that u can help me..=)

[PHP]function invert_matrix($matrix)
{
$size = count($matrix);

if ($size>3)
return false;

if ($size!=count($matrix[0]))
return false;

$I_matrix_I = solve_matrix($matrix);
if ($I_matrix_I==0)
return false;

$adjoint = array();
$inverse = array();
for ($i=0; $i<$size; $i++)
for ($j=0; $j<$size; $j++)
{
$cofactor = array();
for ($k=0; $k<$size; $k++)
{
if ($i!=$k)
{
$temp = array();
for ($l=0; $l<$size; $l++)
{
if ($j!=$l)
array_push($temp, $matrix[$k][$l]);
}
array_push($cofactor, $temp);
}
}
$adjoint[$j][$i] = solve_matrix($cofactor)*pow((-1),($i+$j));
}

for ($i=0; $i<$size; $i++)
for ($j=0; $j<$size; $j++)
$inverse[$i][$j] = $adjoint[$i][$j]/$I_matrix_I;

return $inverse;
}
function solve_matrix($m)
{
$_size = count($m);
switch ($_size)
{
case 1:
return $m[0][0];
case 2:
return (($m[0][0] * $m[1][1]) - ($m[0][1] * $m[1][0]));
case 3:
return ($m[0][0]*($m[1][1]*$m[2][2]-$m[1][2]*$m[2][1])) - ($m[0][1]*($m[1][0]*$m[2][2]-$m[2][0]*$m[1][2])) + ($m[0][2]*($m[1][0]*$m[2][1]-$m[2][0]*$m[1][1]));
default:
return 0;
}
}[/PHP]
Use invert_matrix($matrix) to invert any matrix upto size 3

Regards,
Harpreet