Question 343991
<pre><b>
{{{system(x+y+2z+t=1,
x+2y+z+t=2,
2x+y+z+t=4,
x+y+z+2t=3)}}}

Put in all the 1 coefficients

{{{system(1x+1y+2z+1t=1,
1x+2y+1z+1t=2,
2x+1y+1z+1t=4,
1x+1y+1z+2t=3)}}}

Take out the variables and replace the column
of equal signs by a vertical line:

{{{(matrix(4,6,

1,1,2,1,"|",1,
1,2,1,1,"|",2,
2,1,1,1,"|",4,
1,1,1,2,"|",3))}}}

Do row operations

-1R1+R2->R2

(That means to multiply row 1 temporarily by -1
and add it to row 2, replace row 2 by that, then
restore row 1 as it was):

{{{(matrix(4,6,

1,1,2,1,"|",1,
0,1,-1,0,"|",1,
2,1,1,1,"|",4,
1,1,1,2,"|",3))}}}

-2R1+R3->R3

{{{(matrix(4,6,

1,1,2,1,"|",1,
0,1,-1,0,"|",1,
0,-1,-3,-1,"|",2,
1,1,1,2,"|",3))}}}

-R1+R4->R4

{{{(matrix(4,6,

1,1,2,1,"|",1,
0,1,-1,0,"|",1,
0,-1,-3,-1,"|",2,
0,0,-1,1,"|",2))}}}

-R2+R1->R1

{{{(matrix(4,6,

1,0,3,1,"|",0,
0,1,-1,0,"|",1,
0,-1,-3,-1,"|",2,
0,0,-1,1,"|",2))}}}

R2+R3->R3

{{{(matrix(4,6,

1,0,3,1,"|",0,
0,1,-1,0,"|",1,
0,0,-4,-1,"|",3,
0,0,-1,1,"|",2))}}}

R3->R4
R4->R3
(That means to interchange row 3 and row 4)

{{{(matrix(4,6,

1,0,3,1,"|",0,
0,1,-1,0,"|",1,
0,0,-1,-1,"|",2,
0,0,-4,-1,"|",3))}}}

-R3->R3
{That means to multiply row 3 by -1)

{{{(matrix(4,6,
1,0,3,1,"|",0,
0,1,-1,0,"|",1,
0,0,1,1,"|",-2,
0,0,-4,-1,"|",3))}}}

-3R3+R1->R1

{{{(matrix(4,6,
1,0,0,4,"|",6,
0,1,-1,0,"|",1,
0,0,1,1,"|",-2,
0,0,-4,-1,"|",3))}}}

R3+R2->R2

{{{(matrix(4,6,
1,0,0,4,"|",6,
0,1,0,-1,"|",-1,
0,0,1,1,"|",-2,
0,0,-4,-1,"|",3))}}}

4R3+R4->R4

{{{(matrix(4,6,
1,0,0,4,"|",6,
0,1,0,-1,"|",-1,
0,0,1,1,"|",-2,
0,0,0,-5,"|",-5))}}}

{{{-1/5}}}R4->R4
(That means to multiply row 4 by {{{1/5}}})

{{{(matrix(4,6,
1,0,0,4,"|",6,
0,1,0,-1,"|",-1,
0,0,1,1,"|",-2,
0,0,0,1,"|",1))}}}

-4R4+R1->R1

{{{(matrix(4,6,
1,0,0,0,"|",2,
0,1,0,-1,"|",-1,
0,0,1,1,"|",-2,
0,0,0,1,"|",1))}}}

R4+R2->R2

{{{(matrix(4,6,
1,0,0,0,"|",2,
0,1,0,0,"|",0,
0,0,1,1,"|",-2,
0,0,0,1,"|",1))}}}

-R4+R3->R3

{{{(matrix(4,6,
1,0,0,0,"|",2,
0,1,0,0,"|",0,
0,0,1,0,"|",-1,
0,0,0,1,"|",1))}}}

Place the variables and equal signs back in

{{{system(1x+0y+0z+0t=2,
0x+1y+0z+0t=0,
0x+0y+1z+0t=-1,
0x+0y+0z+1t=1)}}}

Simplify:

{{{system(x=2,
y=0,
z=-1,
t=1)}}}

Edwin</pre>