Do not use numpy or scipy please. Write a program that checks to see if a matrix is symmetric, positive definite and, if so$,$ uses the Cholesky method to solve the matrix equation and if not, uses the Doolittle method. 'Apply your program to the following two problems with your solution vectors printed nicely and an indication of which numerical method was used:

$x_1-x_2+3x_3+2x_4=,15$

$-x_1+5x_2-5x_3-2x_4=,-35$

$3x_1-5x_2+19x_3+3x_4=,94$

$2x_1-2x_2+3x_3+21x_4=,1$

$4x_1+2x_2+4x_3=,20$

$2x_1+2x_2+3x_3+2x_4=,36$

$4x_1+3x_2+6x_3+3x_4=,60$

$2x_2+3x_3+9x_4=,122$