Given are the matrix A and the vector e with A = a a 1 a 1 1 1 1 and c= a a) Determine the determinant of A. In light of this result, for what value(s) of a is the solution to the linear system of equations (LSE) Az = unique? b) Solve the LSE for the case a=0. If a solution exists, give it in vector form. c) For a 0, investigate the rank of A and the rank of the augmented matrix. Are there any values of the parameter a for which the rank of the augmented matrix is greater than the rank of A? For what values of a are there an infinite number of solutions and for what values are there no solutions?