A linear system is described by the following equations:

x13x2+4x32x15x2+6x33x1+3x2+4x3===366

Solve the above linear system by answering the following:

1. (2 Marks) Construct the Frobenius matrices F(1) and F(2) for the above linear system.
2. (2 Marks) Find the unit lower triangular matrix L.
3. (4 Marks) Now find the solution of this linear system using LU-decomposition method. You may use the lower triangular matrix found in the previous question.
4. (2 Marks) Suppose, you have constructed an Augmented matrix from a different linear system as given below,

   200207511164

   Explain why the Gaussian elimination method fails to solve this system? Also explain how we can overcome the problem to actually solve it (you do not have to solve this system)?