Can someone help me solve a row echelon problem pleasee???

Question

thatonegirl_ · Answer

The matrix is
1 2 3
0 1 5
5 6 0

astrophysics · Answer

Heyy

thatonegirl_ · Answer

Heya

astrophysics · Answer

Do you understand what REF and RREF are?

thatonegirl_ · Answer

no, what are they?

astrophysics · Answer

Row Echelon Form and Reduced Row Echelon Form

thatonegirl_ · Answer

Ohh. I know the first one. What is the difference?

thatonegirl_ · Answer

Actually idk if i know that one xD all ik is that i have to "manipulate" the rows to make it identical to the identity matrix, while changing the right side of the matrix (which is originally the identity matrix)

thatonegirl_ · Answer

And then the right side shows the answer. So whatever that is called is what i'm doing :S

astrophysics · Answer

Ah ok, so the first one Row Echelon Form has the three properties:
1. All non zero rows are above any rows of all zeros. 
2. Each leading entry of a row is in a column to the right of the leading entry of the row above it.
3. All entries in a column below a leading entry are zeros.

So then if these properties are satisfied it is in row echelon form, and then to make it reduced we have 2 extra properties.

4. The leading entry in each nonzero row is 1.
5. Each leading 1 is the only nonzero entry in its column.

Looks a bit complex but it really isn't haha. So essentially Row echelon form looks like |dw:1465347734172:dw| where the squiggly line indicates leading entries which can be any non zero value and the dotted entries can be anything