Question 985488

{{{2x+y+2z=0}}}
{{{4x+3y-z=1}}}
{{{5x-4y+3z=-41}}}
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{{{(matrix(3,4,
2,1,2,0,
4,3,-1,1,
5,-4,3,-41) )}}}

Step 1: Swap row {{{3}}} and {{{1}}}
	 
 		
{{{(matrix(3,4,
5,-4,3,-41,
4,3,-1,1,
2,1,2,0) )}}}
 

Step 2: Divide row {{{1}}} by {{{5}}}
 		 
 	 
{{{(matrix(3,4,
1,-0.8,0.6,-8.2,
4,3,-1,1,
2,1,2,0) )}}}


Step 3: Subtract ({{{4 * row {{{1}}}) from row {{{2}}}
 		  
 		
{{{(matrix(3,4,
1,-0.8,0.6,-8.2,
0,6.2,-3.4,33.8,
2,1,2,0) )}}} 

Step 4: Subtract ({{{2}}} * row {{{1}}}) from row {{{3}}}
 		 
	 
 	{{{(matrix(3,4,
1,-0.8,0.6,-8.2,
0,6.2,-3.4,33.8,
0,2.6,0.8,16.4) )}}} 	
 

Step 5: Divide row {{{2}}} by {{{6.2}}}
 		 
	 
 	{{{(matrix(3,4,
1,-0.8,0.6,-8.2,
0,1,-0.548,5.452,
0,2.6,0.8,16.4) )}}} 
 		 

Step 6:
 Subtract ({{{2.6 }}}* row{{{ 2}}}) from row {{{3}}}
 		  
 		
 	{{{(matrix(3,4,
1,-0.8,0.6,-8.2,
0,1,-0.548,5.452,
0,0,2.226,2.226) )}}}  

Step 7: Divide row {{{3}}} by {{{2.226}}}

	 
{{{(matrix(3,4,
1,-0.8,0.6,-8.2,
0,1,-0.548,5.452,
0,0,1,1) )}}} 
 

Matrix is now in row echelon form

Step 8: Subtract ({{{0.6}}} * row {{{3}}}) from row {{{1}}}
 		 
 	
{{{(matrix(3,4,
1,-0.8,0,-8.8,
0,1,-0.548,5.452,
0,0,1,1) )}}} 
  

Step 9: Subtract ({{{-0.548}}} * row {{{3}}}) from row {{{2}}}
 		 
	 
{{{(matrix(3,4,
1,-0.8,0,-8.8,
0,1,0,6,
0,0,1,1) )}}} 

Step 10: Subtract ({{{-0.8}}} * row {{{2}}}) from row {{{1}}}
 		 
	 
 {{{(matrix(3,4,
1,0,0,-4,
0,1,0,6,
0,0,1,1) )}}}		 

Matrix is now in {{{reduced}}}{{{ row}}} echelon form.

solution:

{{{x=-4}}}
{{{y=6}}}
{{{z=1}}}

check:

{{{2x+y+2z=0}}}
{{{2(-4)+6+2*1=0}}}
{{{-8+8=0}}}
{{{0=0}}}