高斯--喬登方法 (對角矩陣) EX6-2

Divide row1 by -1 1 -1 -2 -2 3 -1 1 6 -1 3 4 4 Add (-3 * row1) to row2 1 -1 -2 -2 1 -1 -2 -2 0 2 7 12 -3 3 6 6 -1 3 4 4 3 -1 1 6 0 2 7 12 Add (1 * row1) to row3 1 -1 -2 -2 1 -1 -2 -2 0 2 7 12 -1 3 4 4 0 2 2 2 0 2 2 2 Divide row2 by 2 1 -1 -2 -2 0 2 7 12 0 1 3.50 6 0 1 3.5 6 0 2 2 2 Add (-2 * row2) to row3 1 -1 -2 -2 0 1 3.50 6 0 1 3.50 6 0 -2 -7 -12 0 0 -5 -10 0 2 2 2 0 0 -5 -10 Divide row3 by -5 1 -1 -2 -2 0 1 3.50 6 0 0 1 2 Add (-7/2 * row3) to row2 1 -1 -2 -2 0 0 1 2 0 1 0 -1 0 0 -3.5 -7 0 0 1 2 0 1 3.50 6 0 1 0 -1 Add (2 * row3) to row1 1 -1 0 2 0 0 1 2 0 1 0 -1 0 0 2 4 0 0 1 2 1 -1 -2 -2 1 -1 0 2 Add (1 * row2) to row1 1 0 0  1 1 -1 0 2 0 1 0 -1 0 1 0 -1 0 0 1  2 1 0 0 1
Divide row1 by -1
1	-1	-2	-2
3	-1	1	6
-1	3	4	4
Add (-3 * row1) to row2
1	-1	-2	-2		1	-1	-2	-2
0	2	7	12		-3	3	6	6
-1	3	4	4		3	-1	1	6
					0	2	7	12
Add (1 * row1) to row3
1	-1	-2	-2		1	-1	-2	-2
0	2	7	12		-1	3	4	4
0	2	2	2		0	2	2	2
Divide row2 by 2
1	-1	-2	-2		0	2	7	12
0	1	3.50	6		0	1	3.5	6
0	2	2	2
Add (-2 * row2) to row3
1	-1	-2	-2		0	1	3.50	6
0	1	3.50	6		0	-2	-7	-12
0	0	-5	-10		0	2	2	2
					0	0	-5	-10
Divide row3 by -5
1	-1	-2	-2
0	1	3.50	6
0	0	1	2
Add (-7/2 * row3) to row2
1	-1	-2	-2		0	0	1	2
0	1	0	-1		0	0	-3.5	-7
0	0	1	2		0	1	3.50	6
					0	1	0	-1
Add (2 * row3) to row1
1	-1	0	2		0	0	1	2
0	1	0	-1		0	0	2	4
0	0	1	2		1	-1	-2	-2
					1	-1	0	2
Add (1 * row2) to row1
1	0	0	1		1	-1	0	2
0	1	0	-1		0	1	0	-1
0	0	1	2		1	0	0	1

http://www.gregthatcher.com/Mathematics/GaussJordan.aspx  (EX6-2)

Gauss Jordan Elimination Calculator (convert a matrix into Reduced Row Echelon Form).

Step 2: Enter the values for your matrix, and press the "Solve" button.
  

Divide row1 by -1

1	-1	-2	-2
3	-1	1	6
-1	3	4	4

Add (-3 * row1) to row2

1	-1	-2	-2
0	2	7	12
-1	3	4	4

Add (1 * row1) to row3

1	-1	-2	-2
0	2	7	12
0	2	2	2

Divide row2 by 2

1	-1	-2	-2
0	1	7/2	6
0	2	2	2

Add (-2 * row2) to row3

1	-1	-2	-2
0	1	7/2	6
0	0	-5	-10

Divide row3 by -5

1	-1	-2	-2
0	1	7/2	6
0	0	1	2

Add (-7/2 * row3) to row2

1	-1	-2	-2
0	1	0	-1
0	0	1	2

Add (2 * row3) to row1

1	-1	0	2
0	1	0	-1
0	0	1	2

Add (1 * row2) to row1

1	0	0	1
0	1	0	-1
0	0	1	2