So now we can write our original problem.

So that's my original A right there.

Let's go back to our original equation.

And a real pasta, a real spaghetti, just like bread, never requires animal products.

So let's go back to the original problem.

That's our original y.

Go back to the original equation.

Another way to view it let me rewrite the original equation.

Well this is the inverse of this original matrix.

I will believe that this is the original.

So let me rewrite our original equation.

This is my original A right there.

Our original equation was up here.

So let's just put this into out original equation.

You can find original ways to get things done.

To match the original color, nearly impossible.

So anyway, let's go back to our original matrix.

So what was the original problem I said?

Let's remember our original equation was Ax is equal to b.

When potassium joins, we get to our original one.

And you can just look at the original equation.

Well that's just our original theta that we were dealing with.

By definition it needs to go back to your original a.

And you can actually verify that these satisfy our original equation.

The original apples to oranges ratio is five to eight.

Are you sure this is the original? You didn't make a copy of it, did you?

When X is one Y is 12 when X is three Y is four so we have inverse variation in play.

So this is our original block of our carbon 14.

Let me get my original A, which I've forgotten.

With that said, let me erase that and go back to our original problem.

And so we can go back to our original equation and we could say, wow.

So the inequality stays the same as in our original problem.

So both of these work. And you can put them back into the original equation, to varify it.

So this is just an alternate way of writing this original statement.

We're getting it from our original expression, after we multiplied.

Or we could do it explicitly right over here, we could even go to the original one.

Our original right hand side was just the 2x.

Now, I'm going to start showing you some original techniques that come from the work that I've developed. OK?

I want to live the rest of my life serving you and the princess.

And what was that original matrix that I did in the last video?

And if you want, you can figure out how many of the original grams of ammonia that is.

Or if we look at this distance right here, that was the original problem.

Now, I'm going to start showing you some original techniques that come from the work that I've developed.

Now let's verify that this is the solution to our original equation.

Van Goghs in every room, genuinetype Van Goghs.