But even this reduced level is not sustainable.

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.

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

This is the reduced row echelon form of A.

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

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.

11. The decreased requirement of 60,700 is related to item 2 (b) above.

12. The decreased requirement of 79,200 is related to item 2 (b) above.

So the null space of this guy we could just put in reduced row echelon form the null space of this guy is the same thing as the null space of this guy in reduced row echelon form.

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

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

We got the identity matrix. We put it in reduced row echelon form. We got the identity matrix.

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

By the time you have A as an identity matrix, you have A in reduced row echelon form.

And just like that, we've gotten the A part of our augmented matrix into reduced row echelon form.

This guy's null space is going to be the null space of that guy in reduced row echelon form.

So we know that duplicate rows could never get reduced row echelon form to be the identity.

The right hand side, if the reduced row echelon form here gets to the identity, then the right hand side is going to be the inverse.

Now let's perform another transformation. Let's just do another set of row operations to get us to reduced row echelon form.

We already know from previous videos the reduced row echelon form of something is the identity matrix.

The savings of 5 million represents over 50 per cent of the headquarters staffing reduction.

We put its transformation matrix in reduced row echelon form.

The ratio of a b being the same thing as the ratio of c d.

The reduced amount of 5,800 relates to travel of staff ( 3,800) and supplies and materials ( 2,000), based on expenditure patterns.

But rj I've now replaced. I'm replacing rj with rj minus a scalar multiple of ri. Minus c times ri.

By the time A is like that, your identity matrix, having performed the same exact operations on it, it is going to be transformed into A's inverse.

We know that the ratio we know that the ratio of apples

And I also know that the ratio of boys to girls, the ratio of

This is the rate of change at which x is changing with respect to time.

Aspect ratio

According to the page

Custom ratio

Young people (per cent)

153 157)

Inventory management

Staff ratio

Share ratio

Volume ratio

Charge Percent

Percentage

Author

Kill Percentage

Golden Ratio

(percentage)

COVERAGE