Question

Give the general solution of the equation Ax = b in standard form.

a = [ 2 1 -1 ] b= [ 3 ]

[ 1 2 1 ] [0 ]

[-1 1 2 ] [-3 ]

Answer 1

system is

augmented matrix is

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

convert into Reduced Row Eschelon Form...

Divide row1 by 2

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

Add (-1 * row1) to row2

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

Add (1 * row1) to row3

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

Divide row2 by 3/2

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

Add (-3/2 * row2) to row3

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

Add (-1/2 * row2) to row1

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

reduced system is

...............free variable

general solution is