(Solved): HELP: LU Decomposition (Applied Linear Algebra)The last picture is for LU Decomposition REFERENCE Ut ...

Utilize the following linear system of equations for this activity. $\begin{array}{r}{x}_1+2x_2+3x_3=9\\ 3x_1?x_3=3\\ 2x_1?x_2+x_3=8\end{array}$ Note: Not all matrices have an LU decomposition. However, if the LU decomposition of a matrix doesn't exist, the rows of the matrix can always be permuted to yield a matrix that does have an LU decomposition. Consider the system of equations $Ax=b$ where $A$ does not have an LU decomposition. Let $\mathrm{P}$ be a permutation matrix (a matrix with a single 1 in each row and column). The permuted system of equations $\mathrm{PAx}=\mathrm{Pb}$ still has the same solution, just the order in which the equations are written down is now different. For the correct permutation matrix, the matrix PA will have an LU decomposition. For more information, please see the MATLAB documentation for LU matrix factorization. Script 0 \%Create the coefficient matrix $A$ and and the column matrix $b$ of constants. \%Use the $\mathrm{lu}()$ command to find the LU decomposition of A, storing the lower and upper matrices $\%$ in $L$ and $U$, respectively. \%Solve the system of linear equations $Ax=b$ using the LU decomposition. Store the intermediary $\%$ solution in $y$. Store the solution for $x$ in $x1$. \%Check that the solution $x1$ matches that found by directly using the backslash operator to solve \%the system $Ax=b$. Use the backslash operator to solve $Ax=b$ in one step, storing the solution in $x2$.