Consider the following system of linear equations
x-3y+2z+3w=1
2x-4y+3z+a^(2)w=-1
-3x+y+az-w=b
where
a
and
b
are real numbers. Using Gaussian elimination, determine all possible values of
a
and
b
such that the system has (a) no solution; (b) infinitely many solutions with one free variable; (c) infinitely many solutions with two free variables. Then solve the system in part (c).