Consider the following system of linear equations in variables r, y and z: - U+ x + 2y + = 3 x- v+(3-p)= =P where p is a real parameter. (5.1) Use the Gauss-Jordan elimination method to find a condition on the parameter p such that the linear system above is consistent. (5.2) When the condition in (5.1) is satisfied, find all solutions in terms of p. Important note: Find a condition on the parameter p for which the linear system above has a unique solution and infinitely many solutions respectively, and deduce their solutions for each of these cases. (5.3) Use the definition below to find the rank of the augmented matrix of the linear system when the parameter p = 0. Definition: The rank of a matrix is the maximum number of its linearly independent column vectors (or row vectors). (1.5) Let C and D be m x n matrices, and let X be a vector of order n. Show that (C +D)X = CX + DX