Problem 1. Given the system of linear equations: 3x1 + 12x3 + 24-25 3x+2x2 +16x3 + 4x4 + 2x5 = 2+8x3+2+5x5 2x12+6x3-24 - 5x5 19 = 1 -10 a) Write down the coefficient matrix and the augmented matrix of the system b) Find the Row Echelon form of the augmented matrix. c) Determine the rank of the coefficients matrix and the augmented matrix. d) Without solving the system, determine if it is consistent or inconsistent. Give your explanation in terms of ranks. e) Without solving the system, determine the number of the free variables. Give your explanation in terms of ranks. f) Find the Reduced Row Echelon form of the augmented matrix. g) Solve the system. White down your answer in a vector form.