$"2.$ A linear system is described by the following equations

x

$1$

$$

$+$x

$2$

$$

$+$x

$3$

$$

$2$x

$1$

$$

$+3$x

$2$

$$

$+4$x

$3$

$$

$3$x

$1$

$$

$+4$x

$2$

$$

$+2$x

$3$

$$

$$

$=6$

$=20$

$=17.$

$$

$($a$)(3$ marks$)$ Construct the Frobenius matrices F

$(1)$

and F

$(2)$

from this system. $($b$)(2$ marks$)$ Compute the unit lower triangular matrix L$.($c$)(5$ marks$)$ Now find the solution of the linear system using LU decomposition m XT$01$ ethod. Use the unit lower triangular matrix found in the previous question."