document.write( "Question 316592: Use the Gauss - Jordan method to solve the following system of equations.\r
\n" ); document.write( "\n" ); document.write( "2x + y - z = -1\r
\n" ); document.write( "\n" ); document.write( "x - 2y + 2z = 7\r
\n" ); document.write( "\n" ); document.write( "3x + y + z = 4 \n" ); document.write( "
Algebra.Com's Answer #226513 by CharlesG2(834)\"\" \"About 
You can put this solution on YOUR website!
Use the Gauss - Jordan method to solve the following system of equations.
\n" ); document.write( "2x + y - z = -1
\n" ); document.write( "x - 2y + 2z = 7
\n" ); document.write( "3x + y + z = 4
\n" ); document.write( "-----
\n" ); document.write( "write out the coefficients and the constant as follows:
\n" ); document.write( " x y z c
\n" ); document.write( " 2 1 -1 -1
\n" ); document.write( " 1 -2 2 7
\n" ); document.write( " 3 1 1 4 (add row 3 to row 1)
\n" ); document.write( "-----------------
\n" ); document.write( " 5 2 0 3 (add row 1 to row 2)
\n" ); document.write( " 1 -2 2 7
\n" ); document.write( " 3 1 1 4
\n" ); document.write( "-----------------
\n" ); document.write( " 5 2 0 3
\n" ); document.write( " 6 0 2 10
\n" ); document.write( " 3 1 1 4 (multiply row 3 by -2)
\n" ); document.write( "-----------------
\n" ); document.write( " 5 2 0 3
\n" ); document.write( " 6 0 2 10 (add row 2 to row 3)
\n" ); document.write( " -6 -2 -2 -8
\n" ); document.write( "----------------
\n" ); document.write( " 5 2 0 3
\n" ); document.write( " 6 0 2 10
\n" ); document.write( " 0 -2 0 2 (add row 3 to row 1)
\n" ); document.write( "----------------
\n" ); document.write( " 5 0 0 5 (divide row 1 by 5)
\n" ); document.write( " 6 0 2 10 (divide row 2 by 2)
\n" ); document.write( " 0 -2 0 2 (divide row 3 by -2)
\n" ); document.write( "----------------
\n" ); document.write( " 1 0 0 1 (multiply row 1 by -3)
\n" ); document.write( " 3 0 1 5
\n" ); document.write( " 0 1 0 -1
\n" ); document.write( "----------------
\n" ); document.write( " -3 0 0 -3 (add row 1 to row 2)
\n" ); document.write( " 3 0 1 5
\n" ); document.write( " 0 1 0 -1
\n" ); document.write( "----------------
\n" ); document.write( " -3 0 0 -3 (lastly divide row 1 by -3)
\n" ); document.write( " 0 0 1 2
\n" ); document.write( " 0 1 0 -1
\n" ); document.write( "----------------
\n" ); document.write( " 1 0 0 1
\n" ); document.write( " 0 0 1 2
\n" ); document.write( " 0 1 0 -1 (rearrange these 3 rows)
\n" ); document.write( "-----------------
\n" ); document.write( " 1 0 0 1
\n" ); document.write( " 0 1 0 -1
\n" ); document.write( " 0 0 1 2
\n" ); document.write( "-----------------
\n" ); document.write( "we wanted to get to the last matrix shown, it is the identity matrix, it has a nice neat diagonal of 1's and the answers are all in the last column\r
\n" ); document.write( "\n" ); document.write( "x = 1
\n" ); document.write( "y = -1
\n" ); document.write( "z = 2\r
\n" ); document.write( "\n" ); document.write( "check:
\n" ); document.write( "2x + y - z = -1
\n" ); document.write( "x - 2y + 2z = 7
\n" ); document.write( "3x + y + z = 4\r
\n" ); document.write( "\n" ); document.write( "2(1) + (-1) - (2) = 2 - 1 - 2 = 2 - 3 = -1
\n" ); document.write( "(1) - 2(-1) + 2(2) = 1 + 2 + 4 = 7
\n" ); document.write( "3(1) + (-1) + (2) = 3 - 1 + 2 = 2 + 2 = 4
\n" ); document.write( " \n" ); document.write( "
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