Q$6$: Solve the following system equation using Cholesky LU decomposition method. Using four significant figures in your calculation.

$8x_1+20x_2+16x_3=100$

$20x_1+80x_2+50x_3=250$

$16x_1+50x_2+60x_3=100$

$[A]=[L][L{]}^T$

$\left[\begin{array}{ccccccc}{l}_{11}& 0& 0& l_{22}& 0& l_{32}& l_{33}\end{array}\right]$

$l_{31}$

$l_{31}$

$l_{21}\left[\begin{array}{ccccccc}{l}_{11}& l_{21}& l_{31}& l_{22}& l_{32}& 0& l_{33}\end{array}\right]$

$0$

$0$

#hand solution