Find values of a, b, and c

Question

Find values of a, b, and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.)

x	+	y	=	2
y	+	z	=	2
x	+	z	=	2
ax	+	by	+	cz	=	0

(a) a unique solution

(a, b, c) =

 

 

(b) no solution

(a, b, c) =

 

 

(c) infinitely many solutions

(a, b, c) =

 

 

Answer 1

by observation the point (1,1,1) satisfies first three equations.

now want a+b+c=0 using (1,1,1)

which is satisfied when a+b=-c

choosing any value of c have linear equation for values

of a and b. Infinitely many a and b for infinitely many choices of c.