Question

# A linear system of equations, such as: a_{0,0} x_{0}+a_{0,1} x_{1}+a_{0,2} x_{2}=b_{0} a_{1,0} x_{0}+a_{1,1} x_{1}+a_{1,2} x_{2}=b_{1} a_{2,0} x_{0}+a_{2,1} x_{1}+a_{2,2} x_{2}=b_{2} \text { where }\left[a_{0.0}, a_{0,1}, a_{0,2}, \ldots, a_{2,2}\right] \text { are a subset of } \mathbb{R}, \text { can be written as } A \mathbf{x}=\mathbf{b}, \text { where } A=\left[\begin{array}{lll} a_{0,0} & a_{0,1} & a_{0,2} \\ a_{1,0} & a_{1,1} & a_{1,2} \\ a_{2,0} & a_{2,1} & a_{2,2} \end{array}\right], \quad \mathbf{x}=\left[\begin{array}{l} x_{0} \\ x_{1} \\ x_{2} \end{array}\right], \quad \mathbf{b}=\left[\begin{array}{l} b_{0} \\ b_{1} \\ b_{2} \end{array}\right] The general procedure to solve a linear system of equations is called Gaussian elimination. The idea is to perform elementary row operations to reduce the system to its row echelon form and then solve it. Your task is to write a python script which uses Gaussian elimination to reduce a system of any 3 linear equations with unknown variable to echelon form to solve it. 1. It is critical that you plan the programme flow in terms of elementary row operations. Each type of elementary row operation should be performed via a function call. The function should take appropriate inputs and return the transformed row elements. 2. Your programme should be smart enough to recognise a matrix on which Gaussian elimination method may not be applied.  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5  Fig: 6  Fig: 7  Fig: 8  Fig: 9  Fig: 10