use elementary row operations to reduce the given matrix to (a) row echelon form and (b) reduced row echelon form.
[-2 -4 7
-3 -6 10
1 2 -3]
$\displaystyle \begin{bmatrix}-2&-4&7\\-3&-6&10\\1&2&-3\end{bmatrix}$
I will not show the matrices as I get it into REF, because I want you to put some effort into this; but I will give you the row operations that lead to REF. I leave it for you to discover the row operations to get it into RREF from REF.
1. $\displaystyle R_2\leftrightarrow R_3$
2. $\displaystyle 3R_1+R_2\rightarrow R_2$
3. $\displaystyle 2R_1+R_3\rightarrow R_3$
4. $\displaystyle -R_2+R_3\rightarrow R_3$
Can you take it from here?
--Chris
It is actually one row operation.
Remember that in RREF, the leading 1's have zeros above and below them [except if the leading 1 is in the first row, first column--it would only have zeros below it].
I think this is enough of a hint for you to finish this off...
Can you try to take it from here?
--Chris