Science:Math Exam Resources/Courses/MATH221/December 2009/Question 01/Statement

Consider the system of equations:

$\begin{array}{cccc}{x}_1+& x_2-& -x_3& =2\\ x_1+& 2x_2+& x_3& =3\\ x_1+& x_2+& (c^2-5)x_3& =c\end{array}$

Find all values of c such that the system has:

(a) no solutions

(b) a unique solution

(c) infinitely many solutions

In case c. write the general solution in the parametric vector form.