Consider the square system of linear equations Ax = b with
A = (k 1 2; 2 1 k; k 0 1), b = (1; -7; 3), x = (x1; x2; x3)
where k is an unspecified real parameter.
a) Find all values of k, such that the given system has a unique solution. For which values of k is the matrix A invertible?
b) Find all values of k, such that the given system admits infinitely many solutions and give all values of k for which the system is inconsistent.