Question 735913
given:

{{{(
 matrix( 3,4,
3, -1, -2, 1, 
4, 2,  1,  5, 
6,  -2, -4, 9
 )
)}}}

{{{matrix(3, -1, -2, 1, 
 4, 2,  1,  5, 
 6,  -2,  -4, 9 ))}}}


Row operation
1:  


{{{(matrix( 3,   -1,  	 -2,  	 1, 
 4 , 	 2 , 	 1,  	 5, 
 6 , 	 -2,  	 -4,  	 9 
 )
)}}} ....multiply the 1st row by 1/3	
 => {{{(
 matrix( 1,  	 -1/3,  	 -2 / 3,  	 1 / 3, 
 4  ,	 2 , 	 1,  	 5, 
 6  ,	 -2 , 	 -4 , 	 9  
 )
)}}} 

Row operation
2:  

 {{{(
 matrix( 1,  	 -1/3,  	 -2 / 3,  	 1 / 3, 
 4  ,	 2 , 	 1,  	 5, 
 6  ,	 -2 , 	 -4 , 	 9  
 )
)}}} .........add -4 times the 1st row to the 2nd row...=> {{{(
 matrix( 1 , 	 -1 / 3,  	 -2 / 3,  	 1 / 3, 
 0 , 	 10 / 3,  	 11/  3,  	 11/  3, 
 6 , 	 -2,  	 -4,  	 9 
 )
)}}}


Row operation
3:

{{{(
 matrix( 1 , 	 -1 / 3,  	 -2 / 3,  	 1 / 3, 
 0 , 	 10 / 3,  	 11/  3,  	 11/  3, 
 6 , 	 -2,  	 -4,  	 9 
 )
)}}}..............add -6 times the 1st row to the 3rd row=>..{{{(
 matrix(  1 , 	 -1/  3,  	 -2 / 3,  	 1/  3, 
 0 , 	 10 / 3,  	 11/  3,  	 11 / 3, 
 0,  	 0 , 	 0 , 	 7  
 )
)}}}.

Row operation
4:

{{{(
 matrix( 1 , 	 -1/  3,  	 -2 / 3,  	 1/  3, 
 0 , 	 10 / 3,  	 11/  3,  	 11 / 3, 
 0,  	 0 , 	 0 , 	 7 
 )
)}}}....multiply the 2nd row by 3/10..=>...{{{(
 matrix( 1,  	 -1/  3,  	 -2 / 3,  	 1 / 3, 
 0 , 	 1,  	 11  /10,  	 11 / 10, 
 0,  	 0 , 	 0  ,	 7 
 )
)}}}

Row operation
5:

{{{(
 matrix( 1,  	 -1/  3,  	 -2 / 3,  	 1 / 3, 
 0 , 	 1,  	 11  /10,  	 11 / 10, 
 0,  	 0 , 	 0  ,	 7 
 )
)}}}...........multiply the 3rd row by 1/7...=>...{{{(
 matrix( 1 , 	 -1/  3 , 	 -2 / 3,  	 1 / 3 ,
 0,  	 1 , 	 11 / 10,  	 11 / 10, 
 0 , 	 0 , 	 0,  	 1
 )
)}}}

Row operation
6:

{{{(
 matrix( 1 , 	 -1/  3 , 	 -2 / 3,  	 1 / 3 ,
 0,  	 1 , 	 11 / 10,  	 11 / 10, 
 0 , 	 0 , 	 0,  	 1 
 )
)}}}.....add -11/10 times the 3rd row to the 2nd row...>...{{{(
 matrix(  1,  	 -1/  3,  	 -2/  3,  	 1/  3, 
 0 , 	 1,  	 11/  10,  	 0, 
 0 , 	 0 , 	 0 , 	 1 
 )
)}}}


Row operation
7:
{{{(
 matrix( 1,  	 -1/  3,  	 -2/  3,  	 1/  3, 
 0 , 	 1,  	 11/  10,  	 0, 
 0 , 	 0 , 	 0 , 	 1 
 )
)}}}....add -1/3 times the 3rd row to the 1st row...=>...{{{(
 matrix( 1,  	 -1 / 3,  	 -2 / 3,  	 0, 
 0 , 	 1 , 	 11 / 10,  	 0, 
 0,  	 0,  	 0,  	 1 
 )
)}}}

Row operation
8:

matrix( 1,  	 -1 / 3,  	 -2 / 3,  	 0, 
 0 , 	 1 , 	 11 / 10,  	 0, 
 0,  	 0,  	 0,  	 1 
 )
)}}}.......add 1/3 times the 2nd row to the 1st row....=>

matrix( 1,  	 0 , 	 -3/  10,  	 0 
 0 , 	 1,  	 11/  10 , 	 0, 
 0 , 	 0,  	 0,  	 1
 )
)}}}


so, your solutions ae: {{{x=0}}}, {{{y=0}}}, and {{{z=1}}}