Given the following linear system:

$([2,1,-1,2],[4,5,-3,6],[-2,5,-2,6],[4,11,4,8])([x],[y],[z],[w])=([5],[9],[4],[2])$

$1-$ Describe the algorithm that will transform the matrix equation into an upper triangular system. Describe all the steps in a flowchart. $($Submit the flowchart in a pdf format$)$

$2-$ Implement the algorithm. $($Use Python$)$

$($Submit the $.$py Python code$)$

$3-$ Describe an algorithm that can be used for solving the equation $Ux=b$ where $U$ is an upper triangular matrix.

$4$ Implement the described algorithm in conjunction with the procedure you implemented in $2.$ Solve for $x.$