Question

Solve and explain the process of solving the following system with matrix reduced row-echelon form. Last, explain your results for the following problem:

3x – 4y + 4z =7
x – y – 2z = 2
2x – 3y + 6z = 5

Answer 1

3x – 4y + 4z =7
x – y – 2z = 2
2x – 3y + 6z = 5

for the system the augmented matrix is

3	-4	4	7
1	-1	-2	2
2	-3	6	5

convert matrix in  Reduced Row Eschelon Form...

Divide row1 by 3

1	-4/3	4/3	7/3
1	-1	-2	2
2	-3	6	5

Add (-1 * row1) to row2

1	-4/3	4/3	7/3
0	1/3	-10/3	-1/3
2	-3	6	5

Add (-2 * row1) to row3

1	-4/3	4/3	7/3
0	1/3	-10/3	-1/3
0	-1/3	10/3	1/3

Divide row2 by 1/3

1	-4/3	4/3	7/3
0	1	-10	-1
0	-1/3	10/3	1/3

Add (1/3 * row2) to row3

1	-4/3	4/3	7/3
0	1	-10	-1
0	0	0	0

Add (4/3 * row2) to row1

1	0	-12	1
0	1	-10	-1
0	0	0	0