Question

Solve the linear system of equations Ax = b, and give the rank of the matrix A, where A =

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

b =

1

2

3

Answer 1

augmented matrix is

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

convert into Reduced Row Eschelon Form...

Add (-1 * row1) to row3

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

Add (1 * row2) to row3

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

Divide row3 by 4

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

Add (-2 * row3) to row2

1	1	1	-1	1
0	1	0	0	0
0	0	0	1	1

Add (1 * row3) to row1

1	1	1	0	2
0	1	0	0	0
0	0	0	1	1

Add (-1 * row2) to row1

1	0	1	0	2
0	1	0	0	0
0	0	0	1	1

reduced system is

there are 3 pivot entry at first second and fourth column

hence rank is 3

.

....................free

general solution is