Problem 3. (50pts) Write a program (you can use any programming language) to solve the linear system Ax=b by Gaussian elimination and backward substitution, without any pivoting. Run it as follows (the syntax given below is in Matlab as an example): \[ \begin{array}{l} A=\left[\begin{array}{lllllllllll} 3 & 2 & -4 & ; & -4 & 5 & -1 & ; & 2 & -3 & 5 \end{array} ight] \\ \mathrm{b}=[-5 ; 3 ; 11] \\ x=\text { gauss_elim }(A, b) \\ \end{array} \] Try also \[ \begin{array}{l} A=\left[\begin{array}{lllllllllll} 3 & 2 & -4 & ; & 2 & -3 & 5 & ; & -4 & 5 & -1 \end{array} ight] \\ \mathrm{b}=[-5 ; 11 ; 3] \\ x \text { = gauss_elim }(\mathrm{A}, \mathrm{b}) \\ \end{array} \] which is the first system, but with the equations written in a different order (in this case, it is clear from the output that the program does not do interchange the rows of the augmented matrix since pivoting is not used). In the case \[ \begin{array}{l} A=\left[\begin{array}{lllllllllll} 1 & 2 & 3 & 3 & 5 & 6 & 7 & 7 & 8 \end{array} ight] \\ \mathrm{b}=[-5 ; 3 ; 11] \\ x=\text { gauss_elim }(A, b) \\ \end{array} \] explain what went wrong (hint: what is detA ?). Please submit your code, output, and explanation