# Matrix Operation: Why n^2 Steps Needed for Elimination of First Row?

• johnchau123
In summary, you are attempting to solve a matrix equation with forward elimination. You need to eliminate the first row in order to solve the equation.f

#### johnchau123

In my note, it said that

Counting multiplication and division only, in solving linear equations (matrix operation),

Elimination of first row: total n^2 operations

So, forward elimination operations for the matrix is Σ(2 to n) k^2 = n*(n+1)*(2n+1)/6

I have tried to solve the equations but it seem do not need n^2 steps.

Can anyone tell me conceptually why it needs n^2 operations to eliminate the first row?

Thanks.

You have to eliminate the firsty entry, so you add a multiple of another row - that is n multiplications. Then you need to do the second entry in the row. That is another n multiplications in another row. You do this n times, so that is n*n operations.

You have to eliminate the firsty entry, so you add a multiple of another row - that is n multiplications. Then you need to do the second entry in the row. That is another n multiplications in another row. You do this n times, so that is n*n operations.

But i have the following interpretation

Eliminate the first entry and this is n multiplication
Then, I do it n-1, including the first time.

So, I think it is n*(n-1).

To be honest, I'd like you to say what it is that you're doing precisely. I'm not aware of anytime I'd actually want to eliminate the entire first row (of what, by the way? nxn matrix? Why?)

To be honest, I'd like you to say what it is that you're doing precisely. I'm not aware of anytime I'd actually want to eliminate the entire first row (of what, by the way? nxn matrix? Why?)

The following link is a picture which shows what my note says.