00:01
Hi, to find the hessian matrix for f x y z is equal to ax square plus by square plus cz square.
00:12
Now, the hessian matrix is del square f by del x square, del square f by del x del y, del square f by del x del z, del square f by del y del x, del square f by del y square and del square f by del y del z, del square f by del z del x, del square f by del z del y and del square f by del z square.
00:40
So that means we need to find the second partial derivatives.
00:43
So first we find del f by del x, that is 2 ax, del f by del y will be 2 by, del f by del z will be 2cz, so down del square f by del x square will be 2a, del square f by del x del y will be equal to 0, and del square by del x del z is equal to 0, del square by del y del x is equal to 0, del square f by del y square is 2b, del square f by del y del z is equal to 0.
01:24
Similarly, we have del square f by del z del x equal to 0, del square f by del z del y equal to 0, del square f by del z is equal to 2c.
01:37
So therefore, in this case, the hessian matrix becomes 2a 0 0 0 2b 0 0 0 2c.
01:50
Now in part b, we have g x y z is equal to ax to the power ay to the power bz to the power c...