document.write( "Question 630512: 2x-y+8z=13;3x+4y+5z=18;5x-2y+7z=20;
\n" );
document.write( "x=
\n" );
document.write( "y=
\n" );
document.write( "z=
\n" );
document.write( "solve the following equations through gauss jordan method
\n" );
document.write( " \n" );
document.write( "
Algebra.Com's Answer #396993 by jsmallt9(3759) ![]() You can put this solution on YOUR website! \r\n" ); document.write( "Initial matrix\r\n" ); document.write( " 2 -1 8 13\r\n" ); document.write( " 3 4 5 18\r\n" ); document.write( " 5 -2 7 20\r\n" ); document.write( "\r\n" ); document.write( "Row 1 = Row 1 times 1/2\r\n" ); document.write( " 1 -1/2 4 13/2\r\n" ); document.write( " 3 4 5 18\r\n" ); document.write( " 5 -2 7 20\r\n" ); document.write( "\r\n" ); document.write( "Row 2 = row 2 + -3 times row 1\r\n" ); document.write( " 1 -1/2 4 13/2\r\n" ); document.write( " 0 11/2 -7 -3/2\r\n" ); document.write( " 5 -2 7 20\r\n" ); document.write( "\r\n" ); document.write( "Row 3 = row 3 + -5 times row 1\r\n" ); document.write( " 1 -1/2 4 13/2\r\n" ); document.write( " 0 11/2 -7 -3/2\r\n" ); document.write( " 0 1/2 -13 -25/2\r\n" ); document.write( "\r\n" ); document.write( "Row 2 = Row 2 times 2/11\r\n" ); document.write( " 1 -1/2 4 13/2\r\n" ); document.write( " 0 1 -14/11 -3/11\r\n" ); document.write( " 0 1/2 -13 -25/2\r\n" ); document.write( "\r\n" ); document.write( "Row 1 = row 1 + (1/2) times row 2\r\n" ); document.write( " 1 0 37/11 70/11\r\n" ); document.write( " 0 1 -14/11 -3/11\r\n" ); document.write( " 0 1/2 -13 -25/2\r\n" ); document.write( "\r\n" ); document.write( "Row 3 = row 3 + (-1/2) times row 2\r\n" ); document.write( " 1 0 37/11 70/11\r\n" ); document.write( " 0 1 -14/11 -3/11\r\n" ); document.write( " 0 0 -136/11 -136/11\r\n" ); document.write( "\r\n" ); document.write( "Row 3 = Row 3 times -11/136\r\n" ); document.write( " 1 0 37/11 70/11\r\n" ); document.write( " 0 1 -14/11 -3/11\r\n" ); document.write( " 0 0 1 1\r\n" ); document.write( "\r\n" ); document.write( "Row 1 = row 1 + (-37/11) times row 3\r\n" ); document.write( " 1 0 0 3\r\n" ); document.write( " 0 1 -14/11 -3/11\r\n" ); document.write( " 0 0 1 1\r\n" ); document.write( "\r\n" ); document.write( "Row 2 = row 2 + (14/11) times row 3\r\n" ); document.write( " 1 0 0 3\r\n" ); document.write( " 0 1 0 1\r\n" ); document.write( " 0 0 1 1\r\n" ); document.write( " \n" ); document.write( "So x = 3, y = 1 and z = 1 (from the last column). \n" ); document.write( " |