The partial of this with respect to y is equal to the partial of this with respect to N.

So the partial of this, with respect to y, is different than the partial of N, with respect to x.

What's the partial of N with respect to x?

It was different than N with respect to x.

So psi, with respect to y, is equal to N.

The partial of N, with respect to x, is 2.

This n is the same thing as that n.

So this is n by k, this guy right here is k by n, times an n by k.

The partial of psi, with respect to y, is equal to N.

Rho N with respect to y times each little chunk of area

So if this is n by n, these each are going to be n minus 1 by n minus 1.

The partial of M with respect to y is equal to the partial of N with respect to x.

So instead of just adding N plus 1 N times, we could say that this is just N times N plus 1.

So this is one, two, three and this is n, n reflects these time periods.

But I'm going to call this the identity matrix and I'll call this I sub n, and I called that sub n because it's an n by n identity matrix.

And the partial derivative of psi, with respect to y, is equal to N.

At this time this was an N of 20. Now there's an N of about 100.

This n and this s are constant.

So this is equal to n times x to the n minus 1.

So essentially this would be the top of it and this would be n and this would be n.

N. singalana N. spathulata N. spathulata N. tobaica N. spectabilis N. tobaica Endemic species with no known natural hybrids N. adnata N. junghuhnii N. lavicola N. naga N. tenuis Philippines Nepenthes natural hybrids recorded from the Philippines.

Take the partial with respect to y, and set that equal to our N expression.

And we can define this as 'n' where it's n symbol transfers per second.

So this will have n components.

So this guy has n columns.

What happens if this was n?

In this case, n is 3.

In general, if you have f(x) x n, then this is odd if 'n' is odd, and this is an even function if 'n' is even.

And each of these guys are going to have n terms because you have n columns. So that's another way of writing this same n by n matrix.

And this is going to be a square matrix, where this has to be n, and this has to be n.

Let me define so this is my matrix A. Let me define a submatrix Aij to be equal to see this is n by n, right? So this is going to be an n minus 1 by n minus 1 matrix.

Well, if we're divisible by n 4, we're also divisible by n, since this is one of the factors of n 4

In the next video, we'll try to extend this to n by n square matrices.

So this is a determinant of an n minus 1 by n minus 1 matrix.

Well, you apply this definition again, and then it's going to be in terms of n minus 2 times n or n minus 2 by n minus 2 matrices.

So in this formula right here, this is n.

But we said n this substitution comes into this.

In this case k and n are equal to the same thing, so let's just replace that n, that k with an n.

This is the n th Fibonacci number.

This is m tuples, that's n tuples.

So this is an ordered n tuple.

The partial of N, with respect to x is equal to well, there's no x here, right?

If I'm applying 1 N in this direction and it already has 49 N due to the component of gravity in this direction, then my budging force is 50 N

So this thing right here, which was this matrix. Now let's see if we can extend this to a general n by n matrix.

And obviously if we had n terms here, we'd have to have n vectors here, and we could just make this more general to n.