I would like some assistance with some matrix algebra problem

(a) You are told that the rank of matrix A is equal to 3. (i) What do you understand by this statement? (ii) Suggest a matrix whose largest possible rank is equal to matrix A. Explain your answer. (3 marks) (b) The rank of the matrix A is 2. 4 2 A = k 3 2 2 (i) Determine the value of the constant k. (3 marks) For this value of k, is A invertible? Explain. (1 marks) (c) Determine the definiteness of the quadratic form q(x) = x] +2v6x,*2 + 2x2 (4 marks) (d) Consider the following system of linear equations 2x1 - 3x2 + X3 - 3x4 + 2x5 = 6 2x1 - 3x2 + 5X3 - X4 + X5 = 8 4x3 + 3x4 + 2x5 = 3 -2x1 + 3x2 + 3x3 + 3x4 - 9X5 =-6 (i) Is the following system consistent? Provide a justification for your decision. Ensure that you explain each step in the computation. (11 marks) (ii) Can Cramer's rule and the matrix inversion method be used to solve the system? Justify your response