document.write( "Question 815171: 1. Solve the following equations using Gauss Elimination method.
\n" ); document.write( " 2x+4y+z=3, 3x+2y-2z=-2 , x-y+z=6
\n" ); document.write( "2. Solve the system of equations by Jacobi’s iterative method (calculate three iterations only.)
\n" ); document.write( " 20x+y-2z=17, 3x+20y-z=-18, 2x-3y+20z=25
\n" ); document.write( "3. Find the values of x,y and z using Gauss Seidal method.
\n" ); document.write( " 83x-11y-4z =95 , 7x+52y+13z =104, 3x+8y+29z =71
\n" ); document.write( "4. Solve the system of equations by Gauss Jordan method:
\n" ); document.write( " 3x+2y+7z=4, 2x+3y+z=5, 3x+4y+z=7
\n" ); document.write( "5. Solve the system of equations by matrix inversion method:
\n" ); document.write( " 5x+3y+7z=4, 3x+26y+2z=9, 7x+2y+11z =5
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #490748 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
You should not include so many problems (especially such labor-intensive ones) in a single post. I will do the first one for you. Re-post the others separately if you want more help.

\n" ); document.write( "Note: Algebra.com's formula drawing software does not do matrices very well. So I am going to just show the rectangular array of numbers without the brackets which usually indicate a matrix.

\n" ); document.write( "2x+4y+z=3
\n" ); document.write( "3x+2y-2z=-2
\n" ); document.write( "x-y+z=6
\n" ); document.write( "The augmented matrix:
\n" ); document.write( "

\r\n" );
document.write( "    2    4    1    3\r\n" );
document.write( "    3    2   -2   -2\r\n" );
document.write( "    1   -1    1    6\r\n" );
document.write( "Replace row 1 with 1/2 times row 1:\r\n" );
document.write( "    1    2    1/2    3/2\r\n" );
document.write( "    3    2    -2    -2\r\n" );
document.write( "    1   -1     1     6\r\n" );
document.write( "Add -3 times row 1 to row 2:\r\n" );
document.write( "    1    2    1/2      3/2\r\n" );
document.write( "    0   -4   -7/2    -13/2\r\n" );
document.write( "    1   -1     1       6\r\n" );
document.write( "Add -1 times row 1 to row 3:\r\n" );
document.write( "    1    2    1/2      3/2\r\n" );
document.write( "    0   -4   -7/2    -13/2\r\n" );
document.write( "    0   -3    1/2      9/2\r\n" );
document.write( "Replace row 2 with -1/4 times row 2:\r\n" );
document.write( "    1    2    1/2     3/2\r\n" );
document.write( "    0    1    7/8    13/8\r\n" );
document.write( "    0   -3    1/2     9/2\r\n" );
document.write( "Add -2 times row 2 to row 1:\r\n" );
document.write( "    1    0   -5/4    -7/4\r\n" );
document.write( "    0    1    7/8    13/8\r\n" );
document.write( "    0   -3    1/2     9/2\r\n" );
document.write( "Add 3 times row 2 to row 3:\r\n" );
document.write( "    1    0   -5/4    -7/4\r\n" );
document.write( "    0    1    7/8    13/8\r\n" );
document.write( "    0    0   25/8    75/8\r\n" );
document.write( "Replace row 3 with 8/25 times row 3:\r\n" );
document.write( "    1    0   -5/4    -7/4\r\n" );
document.write( "    0    1    7/8    13/8\r\n" );
document.write( "    0    0    1       3\r\n" );
document.write( "Add 5/4 times row 3 to row 1\r\n" );
document.write( "    1    0    0       2\r\n" );
document.write( "    0    1    7/8     13/8\r\n" );
document.write( "    0    0    1       3\r\n" );
document.write( "Add -7/8 times row 3 to row 2:\r\n" );
document.write( "    1    0    0       2\r\n" );
document.write( "    0    1    0      -1\r\n" );
document.write( "    0    0    1       3\r\n" );
document.write( "

This translates into:
\n" ); document.write( "x = 2
\n" ); document.write( "y = -1
\n" ); document.write( "z = 3 \n" ); document.write( "

\n" );