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

MATH221 December 2009

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### Question 01

Consider the system of equations:

${\begin{matrix}x_{1}+&x_{2}-&-x_{3}&=2\\x_{1}+&2x_{2}+&x_{3}&=3\\x_{1}+&x_{2}+&(c^{2}-5)x_{3}&=c\end{matrix}}$ 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.

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