Question

Give augmented matrix for this system. Find all solutions to this system. Indicate all parameters.

x1-x2+x3+x4=1

2x2+3x3+4x4=2

x1-x2+2x3+3x4=3

x1=? x2=? x3=? x4=?

Answer 1

system is

augmented matrix is

1	-1	1	1	1
0	2	3	4	2
1	-1	2	3	3

convert into Reduced Row Eschelon Form...

Add (-1 * row1) to row3

1	-1	1	1	1
0	2	3	4	2
0	0	1	2	2

Divide row2 by 2

1	-1	1	1	1
0	1	3/2	2	1
0	0	1	2	2

Add (-3/2 * row3) to row2

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

Add (-1 * row3) to row1

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

Add (1 * row2) to row1

1	0	0	-2	-3
0	1	0	-1	-2
0	0	1	2	2

reduced system is

general solution is