# Thread: Unique Solution

1. ## Unique Solution

Consider the following system:
x + y + az = 1
x + ay + z = 4
ax + y + z = b
For which values of a does the system have a unique solution, and for which pairs
of values (a; b) does the system have more than one solution? The value of b does
not have any e ffect on whether the system has a unique solution. Why?

How do I go about doing this? It's already in reduced form. Idk what to do =/

2. Originally Posted by VkL
Consider the following system:
x + y + az = 1
x + ay + z = 4
ax + y + z = b
For which values of a does the system have a unique solution
put that system into a matrix (augmented form), and let the rank of the augmented matrix be equal to the non augmented matrix and equal to the number of variables.

Originally Posted by VkL
and for which pairs
of values (a; b) does the system have more than one solution? The value of b does
not have any e ffect on whether the system has a unique solution. Why?
this a question that you'll probably figure out when you get those ranks, so in this case we require that the rank of the augmented matrix be equal to the non augmented matrix and les than the number of variables.

3. what do you mean

"let the rank of the augmented matrix be equal to the non augmented matrix"?