We have n columns.

combinations may very well fill out the whole nine dimensional space.

Check White posts.

So this guy has n columns.

and each one would be a vector in nine dimensional space and we would

Cypress beams.

We've been writing all of our vectors as columns, so we could call them column vectors, you're just writing them as rows.

We're looking at three pivot columns right now, but it's true if we had n pivot columns.

What are the columns of the new matrix?

Mr. Carter, here is a three column headline in the Chronicle.

The pillars of heaven tremble and are astonished at his rebuke.

The pillars of heaven tremble and are astonished at his reproof.

These are the columns for the a, so it's equal to the matrix

This is actually called a row vector.

It has 2 rows, 1, 2, and 3 columns.

So these guys right here are the columns of my matrix.

those nine columns.

So we have 1, 2, 3, 4 columns.

I look up to the ceiling, I see

Only the Wall in Wall Street, dearie. The little poodle works for him. Mmmhmm?

So this guy could have n column vectors.

Well it has 3 pivot entries, or 3 pivot columns.

I'm going to have 35 did I say cube squares. I have 5 squares in this direction, 7 in this direction. So I'm going to have 35 total squares.

There should be some white posts soon. Pull your head in.

So the columns of this new matrix are ca1, ca2, all the way to can.

So A is a 2 by 3 matrix, 2 rows, 3 columns.

Well, some people say there are oil plumes.

And just to make a few points here, this has exactly 4 columns.

You say which columns have my pivot entries or are associated with pivot variables?

In transpose, you just turn the rows into columns and the columns into rows.

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

We know that the diagonals of a rhombus are perpendicular bisectors we know that that's a right angle,

And I'm going to make them a little strange looking just so you see that you don't always have to do it into nice, clean columns.

All the pillars of the court around shall be filleted with silver their hooks of silver, and their sockets of brass.

All the pillars round about the court shall be filleted with silver their hooks shall be of silver, and their sockets of brass.

I could say this right here, that's v1, then I'm going to have v2, and I have n columns.

I think you get the point. You'd have exactly nine elements and you'd have three rows of three columns.

I can just write them as columns. u1 times u1 is u1 squared. u1 times u2 is u1, u2. u2 times u1 is u2 times u1.

It was shadowy, but it was light enough from the streetlight so I could see it.

And then notice, we got a 2 by 4 matrix, which is the number of rows in A times the number of columns in B.

And I figured out which of these columns in my reduced row echelon form of A, are pivot columns.

Is it going to take a submarine ride to see if there are really oil plumes?

You shall hang it on four pillars of acacia overlaid with gold their hooks shall be of gold, on four sockets of silver.

And thou shalt hang it upon four pillars of shittim wood overlaid with gold their hooks shall be of gold, upon the four sockets of silver.

And just like that, all my numbers in each column, if I were to draw columns like this, divide them up.