Reduce the matrix to reduced row-echelon row

Question

-3  1  -3  21

 2  3   3  -6

 2  0  -3  3

 

Answer 1

Dalla:

 

1) multiply the 1st row by -1/3.  (1, -(1/3) 1, 7), other rows same

 

2) add -2 times the 1st row to the 2nd row.  First and the rows same as in 1), second row = (0. 11/3, 1, 8)

 

3) add -2 times the 1st row to the 3rd row. First and second rows the same as in 2), Third = (0. 2/3, -5, 17)

 

4) multiply the 2nd row by 3/11.First and third rows the same as in 3). Second = (0, 1, 3/11, 24/11)

 

5) add -2/3 times the 2nd row to the 3rd row. First and second the same as in 4). Third = (0, 0, -57/11, 171/11)

 

6) multiply the 3rd row by -11/57. First and second same. Third = (0. 0, 1, -3)

 

7) add -3/11 times the 3rd row to the 2nd row. First and third same. Second = (0, 1, 0 , 3)

 

8) add -1 times the 3rd row to the 1st row. Second, third the same. First = (1, -1/3, 0, -4)

 

9) add 1/3 times the 2nd row to the 1st row. Second, third, same. First = (1, 0, 0, -3)

 

Final answer:

 

1    0     0      -3

0    1     0       3

0    1     1      -3

 

Thank me for the painstaking help!

 

Dr. G.