document.write( "Question 686473: This is about Gauss/Jordan Elimination.What are the value of x,y,w and z in the given equation: x+2y-w+z=9 2x-y+2w+3z=-3 3x+y+w-z=-4 x-y-3w+z=4 \n" ); document.write( "

Algebra.Com's Answer #424804 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
x+2y-w+z=9 2x-y+2w+3z=-3 3x+y+w-z=-4 x-y-3w+z=4\r
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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 -2\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 -2\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( "Multiply Row 1 by -1\r\n" );
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document.write( "Add Row 1 to row 4\r\n" );
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document.write( "Divide Row 1 fo -1\r\n" );
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document.write( "Multiply row 2 by -1\r\n" );
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document.write( "Add row 2 to row 3\r\n" );
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document.write( "Multiply Row 2 by 3 and Row 4 by 5\r\n" );
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document.write( "Add Row 2 to Row 4\r\n" );
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document.write( "Swap rows 3 and 4\r\n" );
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document.write( "Now we have only 0's under the diagonal,\r\n" );
document.write( "so we 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 z\r\n" );
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document.write( "Substitute  into the 3rd equation and solve for w\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,w,z) = (-1,3,-2,2)\r\n" );
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document.write( "Edwin

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