Is the Matrix Symmetric Positive Definite for Cholesky Decomposition?

[fonseh]

Homework Statement

Here's the question :
1x1+ 2x2 +0x3 + 0x4 = 1
2x1+ 9x2 +1x3 + 0x4 = 6
0x1+ 1x2 +9x3 + 4x4 = 2
0x1+ 0x2 +4x3 + 3x4 = 8

I' m asked to solve this question using Choelsky method ( We need the symmetric positive definite matrix when we are using this method)

Homework Equations

The Attempt at a Solution

matrix A = $$\begin{bmatrix}
1 & 2& 0 & 0 \\
2 & 9 & 1 & 0 \\\
0 & 1 & 9 & 4 \\
0 & 0 & 4 & 3
\end {bmatrix} $$

the book stated that for the positive symmetric matrix , we need to ensure that max a_kj less than max a_ii ,
But , in this example , i found that the a_44 which is 3 is less than a_43 which is 4 ... So , how could this be symmetric positive definite matrix ?
How is it possible to solve using Choelsky method ?

 

[BvU]

I' m asked to solve this question using Choelsky method

The guy is called Cholesky.

But it's clear what you are being asked, so go to work and see if and where it goes wrong !

 

[fonseh]

question solved