Chapter 6, Problem 4PS

(a)

To determine

To calculate: The values of $a,b$, and $c$, such that, the system of linear equations, $x+y=2$, $y+z=2$, $x+z=2$, and $ax+by+cz=0$, has a unique solution.

(b)

To determine

To calculate: The values of $a,b$, and $c$, such that, the system of linear equations, $x+y=2$, $y+z=2$, $x+z=2$, and $ax+by+cz=0$, has no solution.

(c)

To determine

To calculate: The values of $a,b$, and $c$ such that, the system of linear equations, $x+y=2$, $y+z=2$, $x+z=2$, and $ax+by+cz=0$, has an infinite number of solutions.