2. Consider the following system of equations in x, y, z where k is an unknown constant: x + 2y 2 = 2 2x + 2ky + 42 0 -X 2y + 2kz = k 6. = = (a) Write the system in the form Ax = b. (b) Calculate det(A) |A|. Find the values of k for which the system has a unique solution. (c) Perform row operations on the augmented matrix [A]b] to determine i. for what value(s) of k the system has no solutions. ii. for what value(s) of k the system has infinitely many solutions. (d) Find the solution(s) when k = 2. (e) Consider the system Ax = 0 when k = case? 1/2. What type of solution exists in this