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The first set of row operations was this. It got us here.

So the whole time we did here, when we did our first row operation.

It's to split the functions of a monopoly line ministry up into three.

We got here by performing some row operations.

When you just performed the same exact row operations you performed on A to get to the identity matrix, if you performed those same exact row operations on the identity matrix, what do you get?

Now, our last row operation we represented with the matrix product S3.

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But you perform a bunch of row operations on all of them.

Now, if we perform that same set of row operations on the identity matrix, what are we going to get?

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And we said those row operations were completely equivalent to multiplying this guy right here by multiplying our original transformation matrix by a series of transformation matrices that represent our row operations.

And we've done this multiple times. You just perform a bunch of row operations.

So I'm saying that my row operation I'm going to perform is equivalent to a linear transformation on the column vector.

Now if you performed that same row operation on this guy right there, what would you have?

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

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