Reduced row echelon form.

That form I'm doing is called reduced row echelon form.

So as we put this into reduced row echelon form, were actually just putting matrix A into reduced echelon form.

left hand side into reduced row echelon form.

You literally put A in reduced row echelon form, so this matrix R is just a reduced row echelon form of A.

This is the reduced row echelon form of A.

Let's call that reduced row echelon form of A.

So what's the reduced row echelon form of B?

That's just the style of reduced row echelon form.

So let's put this in reduced row echelon form.

We have our matrix in reduced row echelon form.

They can take the form of direct subsidies, reduced interest rates or reduced costs for acquiring land.

This became the identity matrix, or reduced row echelon form.

I have essentially put this in reduced row echelon form.

We put its transformation matrix in reduced row echelon form.

But we saw before, we could put into reduced form.

This is the reduced row echelon form of our matrix,

When I put them in reduced row echelon form, and I did that over here, this is the reduced row echelon form of A, I can

The left hand side would go into reduced row echelon form.

That right there is the reduced row echelon form of A.

This almost looks like the identity matrix or reduced row echelon form.

And there we've actually put our matrix in reduced row echelon form.

And now I have my augmented matrix in reduced row echelon form.

Now, we still haven't gotten this guy into reduced row echelon form.

This is just the style, the convention, of reduced row echelon form.

Now, I want to get this augmented matrix into reduced row echelon form.

So I'm almost done, but I'm still not in reduced row echelon form.

What I can do is put this guy into reduced row echelon form.

What you can do is you put it in reduced row echelon form.

So what is the null space of this is the same thing as the null space of this in reduced row echelon form So let's put it in reduced row echelon form.

And when this becomes an identity matrix, that's actually called reduced row echelon form.

So this is let me just say the reduced row echelon form of A.

There's my augmented matrix, now let's put this guy into reduced row echelon form.

So this left hand side will be the reduced row echelon form of A.

That all of the pivot columns in reduced row echelon form are linearly independent.

The number of non pivot columns in the reduced row echelon form of A.

let me put this in reduced row echelon form and find the solution set.

When you put something in reduced row echelon form, let me do it up here. Actually, let's just finish what we started with this guy. Let's put this guy in reduced row echelon form.

Take A, put it into reduced row echelon form, see which columns are pivot columns.

The set of pivot columns for any reduced row echelon form matrix is linearly independent.

The reduced row echelon form of A times our vector x is equal to 0.

Now, what can we do if we want to get to reduced row echelon form?

So this is the reduced row echelon form of B is equal to that right there.

I have this matrix A here that I want to put into reduced row echelon form.

Let's see if we can get this into reduced row echelon form. So what is this?