 #1
 141
 2
 Homework Statement:

Find when the system of equations is unique:
xy2z2w= 3
y+z+w= 4a+3
z+3w= 4a4
(a+2)w= b+4a^24a7
 Relevant Equations:
 Full Rank = Unique
It makes sense that a=2 would cause problems because then we wouldn't have a matrix of full rank and we'd be unable to determine a value for w. But the key also says that when b+4a^24a7≠0. Why is that an issue? For example, if a=1, that just says implies that w=0. Through backsubsitution, we get z=8, y=15, x=2. And the solution: (2, 15,8, 0) is unique still because it's the only possible solution, right?
What am I missing here?
What am I missing here?