document.write( "Question 256455: use the Gauss-jordan method to solve the equation\r
\n" ); document.write( "\n" ); document.write( "x+3y-5z-w=9
\n" ); document.write( "4x+y+3z=4w=11
\n" ); document.write( "-3x-y+z-5w=-23
\n" ); document.write( "x-y-3z-4w=-11
\n" ); document.write( "(type an exact answer in simplified form. if the solution is theempty set, type N for each coordinate where z represents all real numbers) \n" ); document.write( "

Algebra.Com's Answer #188584 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Put in all the 1's\r\n" );
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document.write( "Erase the letters and the plus signs,\r\n" );
document.write( "put a bar where the equal signs are, \r\n" );
document.write( "and put the whole thing in parentheses:\r\n" );
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document.write( "The idea is to get all 0's below the diagonal.\r\n" );
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document.write( "Caution: \r\n" );
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document.write( "1. After you've finished getting zeros under the diagonal\r\n" );
document.write( "in column 1, NEVER USE ROW 1 AGAIN!\r\n" );
document.write( "2. After you've finished getting zeros under the diagonal\r\n" );
document.write( "in column 2, NEVER USE ROW 2 AGAIN!\r\n" );
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document.write( "Multiply the Row 1 by -4\r\n" );
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document.write( "Add Row 1 to Row 2\r\n" );
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document.write( "Divide Row 1 by -4\r\n" );
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document.write( "Multiply Row 1 by 3\r\n" );
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document.write( "Add Row 1 to Row 3\r\n" );
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document.write( "Divide Row 1 by -3\r\n" );
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document.write( "Add Row 1 to row 4\r\n" );
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document.write( "Multiply Row 4 by 2\r\n" );
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document.write( "Add Row 3 to Row 4\r\n" );
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document.write( "Divide Row 3 by 2\r\n" );
document.write( "Divide Row 4 by 2\r\n" );
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document.write( "Multiply Row 2 by 4\r\n" );
document.write( "Multiply Row 3 by 11\r\n" );
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document.write( "Add Row 2 to Row 3\r\n" );
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document.write( "Multiply Row 4 by 3\r\n" );
document.write( "Divide Row 2 by 4\r\n" );
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document.write( "Add Row 3 to Row 4\r\n" );
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document.write( "Now put the letters and the equal signs back in-\r\n" );
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document.write( "Erase all the 0's and the 1's\r\n" );
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document.write( "Solve the 4th equation for w\r\n" );
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document.write( "Substitute  into the 3rd equation and solve for z\r\n" );
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document.write( "Substitute  and  into the 2nd \r\n" );
document.write( "equation and solve for y:\r\n" );
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document.write( "Substitute , , and \r\n" );
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document.write( "So the solution is (x,y,z,w) = (0,1,-2,4)\r\n" );
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document.write( "Edwin

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