Rank , Kernel

Question 2: Rank, Kernel > restart: with (LinearAlgebra) : Assume we know that the vectors > u := (2, 0, - 1, 1, 3) : v := (1, 2, - 1, 2, 1) : are solutions of a linear system of equations A.X=b with matrix of coefficients A. Let we also know that the rank of the augmented matrix Ab=(A b) is 4. a. Using this information, can you say (i) what is the rank of the matrix of coefficients A? Explain. (ii) how many equations are in the system? Explain. (iii) how many variables are in this system? Explain. (iv) how many variables are free (if any)? Explain. b. Find another solution of this inhomogeneous system if possible (explain!), otherwise argue why it is impossible