Solve the following linear systems by
(i) Gaussian Elimination with Back Substitution;
(ii) The Gauss-Jordan algorithm to convert the augmented matrix to the fully reduced form ( 1 | x) with solution x;
(iii) Computing the inverse of the coefficient matrix, and then multiplying it with the right hand side. Keep track of the number of arithmetic operations you need to perform to complete each computation, and discuss their relative efficiency.
(a) x - 2y = 4
3x + y = -l
(b) 2x - 4y + 6z = 6
3x-3y + 4z = -1
-4.v + 3y - 4z = 5
(c) x - 3y =1
3x -1 y + 5z = -1
- 2x + 6y - 5z = 0.