Question

Find the solution set of the linear system: {█(■(

x_1+x_4=260

-x_3+x_4+x_5=-200

x_2+x_3=300

x_1-x_2-x_5=150

Answer 1

augmented matrix is

1	0	0	1	0	260
0	0	-1	1	1	-200
0	1	1	0	0	300
1	-1	0	0	-1	150

convert into Reduced Row Eschelon Form...

Add (-1 * row1) to row4

1	0	0	1	0	260
0	0	-1	1	1	-200
0	1	1	0	0	300
0	-1	0	-1	-1	-110

Swapping row3 with row2

1	0	0	1	0	260
0	1	1	0	0	300
0	0	-1	1	1	-200
0	-1	0	-1	-1	-110

Add (1 * row2) to row4

1	0	0	1	0	260
0	1	1	0	0	300
0	0	-1	1	1	-200
0	0	1	-1	-1	190

Divide row3 by -1

1	0	0	1	0	260
0	1	1	0	0	300
0	0	1	-1	-1	200
0	0	1	-1	-1	190

Add (-1 * row3) to row4

1	0	0	1	0	260
0	1	1	0	0	300
0	0	1	-1	-1	200
0	0	0	0	0	-10

Divide row4 by -10

1	0	0	1	0	260
0	1	1	0	0	300
0	0	1	-1	-1	200
0	0	0	0	0	1

Add (-200 * row4) to row3

1	0	0	1	0	260
0	1	1	0	0	300
0	0	1	-1	-1	0
0	0	0	0	0	1

Add (-300 * row4) to row2

1	0	0	1	0	260
0	1	1	0	0	0
0	0	1	-1	-1	0
0	0	0	0	0	1

Add (-260 * row4) to row1

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

Add (-1 * row3) to row2

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

reduced system is

from last column equation is

which is not possible

hence system has no solution