For what values of c does the following system of linear equations have no solution, a unique solution, infinitely many solutions.
x + 2y − 3z = 4
3x − y + 5z = 2
4x + y + (c^2 − 14)z = c + 2.
Show that in case of infinitely many solutions, the solution may be written as ( 8/ 7 − α, 10 /7 + 2α, α) for any real α.
