![\"\"](\"/images/stars/stars-09.gif\")
You can put this solution on YOUR website!
There is no one way to solve an augmented matrix.
\n" ); document.write( "You have to use row operations to try and get one of the rows with a coefficient of 1.
\n" ); document.write( "For example a 3x3 augmented matrix:
\n" ); document.write( "[1 -2 3 | 9]
\n" ); document.write( "[0 1 3 | 5]
\n" ); document.write( "[0 0 1 | 2]
\n" ); document.write( "The last row tells us that z=2.
\n" ); document.write( "So we can go back and substitute that into our second equation which is:
\n" ); document.write( "
\n" ); document.write( "Then we could substitute both y and z into the first equation to get what x is equal to.
\n" ); document.write( "The row operations you are allowed to do are:
\n" ); document.write( "1. Interchange two rows. (So, just move row 1 down and row 2 up)
\n" ); document.write( "2. Multiply a row by a non-zero constant (So, fractions and any whole numbers)
\n" ); document.write( "3. Add a row to another (So, row 1 + row 2 can be the new row 2. You can also multiply row 1 by something while adding it to row 2, like
\n" ); document.write( "\n" ); document.write( "Unfortunately, all of these operations are done by trial and error to try to get the augmented matrix to look something like the example, where you get z=some number.
\n" ); document.write( "The example problem I referenced had row 3 start out as: [2 -5 5 | 17], and about 5 steps later looked like the example.
\n" ); document.write( "So, you've got a bit of work to solve these things.
\n" ); document.write( "Hope this helps a bit, otherwise post the problem you're having trouble with. \n" ); document.write( "