Problem 4. An electric circuit is given as following and the system of equations was generated by applying the mesh current law to the system: (note: Iz is -10 A). 551,-251=-200 4 3713-414=-250 -251-41, +291₁ = 100 Where I1, 13, and 14 are the loop current as indicated in the figure 100 www D ww 10.A 200 D 25 Ռ ww 250 100 V D MAA 8A a) Set up equations in matrix form and take coefficient matrix to do following: i) Calculate determinant "by hand" and using MATLAB to verify your answer. ii) Use MATLAB to find the inverse and verify the answer. b) Put the system equations in the matrix form and do following: i) Does this system of equations have a unique solution? How do you know? ii) Is this system of equations ill-conditioned? Can you explain why? c) Solve system of equation by: i) Using Cramer's rule. ii) Using Gauss-Seidel iterative method. Try to start at guessing point [ 1 1 1 ] till the results converge to the relative percent error 5%. iii) Using any method to get the most accurate answers to the 6 decimals.