document.write( "Question 592297: Rewrite the system of equations as an augmented matrix. Then simplify the matrix to reduced row echelon form. Identify the solution to the system of equations;\r
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\n" ); document.write( "4x - 2y + 3z = 5
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Algebra.Com's Answer #375916 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "  x +  y +  z = 3\r\n" );
document.write( " 2x -  y +  z = 2\r\n" );
document.write( " 4x - 2y + 3z = 5\r\n" );
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document.write( " 1x + 1y + 1z = 3\r\n" );
document.write( " 2x - 1y + 1z = 2\r\n" );
document.write( " 4x - 2y + 3z = 5\r\n" );
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document.write( "The idea is to use row operations to get it to this form \r\n" );
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document.write( "Add -2Śrow1 to 1Śrow2 to get a 0 where the 2 is on the left\r\n" );
document.write( "of row2:\r\n" );
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document.write( "\"matrix%283%2C1%2C-2%2C1%2C%22%22%29\" = \r\n" );
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document.write( "Add -4Śrow1 to 1Śrow3 to get a 0 where the 4 is on the left\r\n" );
document.write( "of row3:\r\n" );
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document.write( "\"matrix%283%2C1%2C-4%2C%22%22%2C1%29\" = \r\n" );
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document.write( "Add 1Śrow2 to 3Śrow1 to get a 0 where the 1 is on row1 2nd elementt\r\n" );
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document.write( "\"matrix%283%2C1%2C3%2C1%2C%22%22%29\" = \r\n" );
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document.write( "Add -2Śrow2 to 1*row3 to get a 0 where the -6 is:\r\n" );
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document.write( "\"matrix%283%2C1%2C%22%22%2C-2%2C1%29\" = \r\n" );
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document.write( "Add -2Śrow3 to 1*row1 to get a 0 where the 2 is:\r\n" );
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document.write( "\"matrix%283%2C1%2C1%2C%22%22%2C-2%29\" = \r\n" );
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document.write( "Add 1Śrow3 to 1*row2 to get a 0 where the -1 is:\r\n" );
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document.write( "\"matrix%283%2C1%2C%22%22%2C1%2C1%29\" = \r\n" );
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document.write( "We have all the 0's placed, so all we need do is get the 1's\r\n" );
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document.write( "Get a 1 where the first 3 on row1 is by dividing R1 by 3\r\n" );
document.write( "Get a 1 where the first -3 on row2 is by dividing R2 by -3\r\n" );
document.write( "\"matrix%283%2C1%2C%22%F73%22%2C%22%F7-3%22%2C%22%22%29\" = \r\n" );
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document.write( "This is the row-reduced echelon form.  To get the solution, translate\r\n" );
document.write( "it into a system of 3 equations and 3 variables:\r\n" );
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document.write( " 1x + 0y + 0z = 1\r\n" );
document.write( " 0x + 1y + 0z = 1\r\n" );
document.write( " 0x + 0y + 1z = 1\r\n" );
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document.write( "or\r\n" );
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document.write( "x = 1\r\n" );
document.write( "y = 1\r\n" );
document.write( "z = 1\r\n" );
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document.write( "So the solution is (x,y,z) = (1,1,1)\r\n" );
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document.write( "Edwin
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