how to solve thi matrics by using gauss elimination[(x+y-z=0),(2x-y+z=6),(3x+2y-4z=-4)]

Question

my background is not mathematics

Answer 1

Matrix representation of problem:

(  1 1 -1 | 0 )

(  2 -1 1 | 6 )

(  3 2 -4 | -4 )

In the following solution, only the rows that are changed are shown with each operation:

R1+R2: ( 3 0 0 | 6 ); R1/3: ( 1 0 0 | 2 ); R2-2R1: ( 0 -1 1 | 2 ); R3-3R1: ( 0 2 -4 | -10 ); R3/2: ( 0 1 -2 | -5 );

R3+R2: ( 0 0 -1 | -3 ); -R3: ( 0 0 1 | 3 ): R2-R3: ( 0 -1 0 | -1 ): -R2: ( 0 1 0 | 1 ).

Solution:  x=2; y=1; z=3. Check solution:

( 2 1 -3 | 0 )

( 4 -1 3 | 6 )

( 6 2 -12 | -4 )

Rows sum correctly.