I have another question regarding another problem. The system is:
x + y = 0
y + z = 0
x + z = 0
ax + by + cz = 0
Find values for a, b, and c so that the system has:
(a) a unique solution
(b) no solution
(c) an infinite number of solutions
I know for a fact it is not possible for this system to have no solution. It has the trivial solution x = y = z = 0. Also, it seems if a + b + c != 0, then it may have an infinite number of solutions. To be honest aside from already knowing part b, I am not quite certain how to proceed. Thanks again for help!
Of course, x+ z= 0 and x- z= 0 can only be true if x= z= 0. Then x+ y= 0 immediately gives y= 0. That has nothing at all to do with "ax+ by+ cz= 0", except that it is also satisifed by x= y= z= 0. The system has only the single solution x= y= z= 0 no matter what a, b, c are.