Modify the LU Factorization Algorithm so that it can be used to solve a linear system, and then

solve the following linear systems.

a$.$

$1\mathrm{.}012x_1-2\mathrm{.}132x_2+3\mathrm{.}104x_3=1\mathrm{.}984,$

$-2\mathrm{.}132x_1+4\mathrm{.}096x_2-7\mathrm{.}013x_3=-5\mathrm{.}049,$

$3\mathrm{.}104x_1-7\mathrm{.}013x_2+0\mathrm{.}014x_3=-3\mathrm{.}895$

b$.$

$2x_1+x_2=0,$

$-x_1+3x_2+3x_3=5,$

$2x_1-2x_2+x_3+4x_4=-2,$

$-2x_1+2x_2+2x_3+5x_4=6$