In these problems, the last two digits of your student number will be significant. Let $N_1$ be a number equal to the last digit of your student number, $N_2$ be a number equal to the last two digits of your student number. That is$,$ if the last two digits of your student number is $83$ then, $N_1=3,N_2=83.$ Please show each step of your answers in your homework paper clearly.

How many solutions does the following system of linear equations have? Explain!

$x-y+N1z=12$

$-x+3y+z=25$

$3z-4y+2x=26$

Consider the system of equations written as a matrix

Equation:

$-2x+y-0\mathrm{.}3z=0\mathrm{.}1$

$2y+N1x-0\mathrm{.}3z=6\mathrm{.}73$

$3\mathrm{.}8x-0\mathrm{.}7y+2z=5\mathrm{.}9$

Solve the system using Gauss Elimination, Gauss$-$Jordan methods and LU decomposition.

$3.$ The LU decomposition of a matrix A is given as follows:

$L=\left[\begin{array}{ccc}1& 0& 0\\ -5& 1& 0\\ -9& 2& 1\end{array}\right]$ and $U=\left[\begin{array}{ccc}1& 8& 12\\ 0& N1& 6\\ 0& 0& 5\end{array}\right]$

What is $A?$

$4.$ Find the inverse of a matrix A by using LU decomposition.

$5.$ Write MATLAB script for each question given above.