Triangular pyramid

The shape is triangular.

They always make a triangular roof.

So what does upper triangular look like?

The upper triangular everything below the diagonal.

I want to do it in upper triangular form.

Now let's try to get this into upper triangular form.

This is another of what we call an upper triangular matrix.

And just like that, we have a determinant of a matrix in upper triangular form.

The other realization we had was that these upper triangular matrices, you can figure out their determinant.

To get this guy into upper triangular form, it'd be nice to get this to be a 0.

This whole class, where you have 0's below the main diagonal, these are called upper triangular matrices.

So its upper triangular matrix if you want to evaluate this determinant, you just multiply these entries right here.

Then upper triangular, everything below the diagonal is a 0, and everything above the diagonal probably isn't a 0, but you never know.

This is the view from my apartment, over the sort of landscape of triangular balconies that our client called the Leonardo DiCaprio balcony.

And it actually turns out it tends to be computationally more efficient to use these takeaways to put things into upper triangular form first.

I won't prove it here, but you can use the exact same argument you used in the video that I just did on the upper triangular.

And I didn't touch on it in that video, but there is also such a thing as a lower triangular, that you might have guessed how it looks.

But now as the rat explores around, each individual cell fires in a whole array of different locations which are laid out across the environment in an amazingly regular triangular grid.

And you could use the same argument we made in the last video to say that the same is true of the lower triangular matrix, that its determinant is also just the product of those entries.

So given this, that the determinant of this is just the product of those guys, and that I can perform row operations on this guy and not change the determinant, maybe a simpler way to calculate this determinant is to get this guy into an upper triangular form, and then just multiply the entries down the diagonal.