If I have the following matrix (3x3):

1 0 1 5

0 1 0 -7/5

0 0 5 7

Is it legal to just take 1/5 of row 3 and say my new matrix is then:

1 0 1 5

0 1 0 -7/5

0 0 1 7/5

? I'm assuming not bc ive checked my work a hundred times and this could be the only possible mistake (Note I am trying to get it in RREF)

EDIT:

Meh, actually I think you CAN... so who wants to help me find out where I went wrong:

ORIG MATRIX:

1 -1 0 5

-1 1 5 2

0 1 1 0

Then switch R_2 and R_3

1 -1 0 5

0 1 1 0

-1 1 5 2

Then R_3 + R_1

1 -1 0 5

0 1 1 0

0 0 5 7

Then R_1 + R_2

1 0 1 5

0 1 1 0

0 0 5 7

Then R_2 - 1/5R_3

1 0 1 5

0 1 0 -7/5

0 0 5 7

Then 1/5R_3

1 0 1 5

0 1 0 -7/5

0 0 1 7/5

Then R_1 - R_3

1 0 0 18/5

0 1 0 -7/5

0 0 1 7/5

No idea