Question

Hi

Given the following system of linear equations;
ax + y + z = 1,
x + ay + z = a,
x + y + az = a^2

find the values of the real constant, a, for which the system has a unique solution.

Thanks for the help.

Answer 1

a=1

Answer 2

Lemme try this:
Add all three equations:
(a+2)x+(a+2)y+(a+2)z=a^2+a+1
(x+y+z)(a+2)=a^2+a+1
x+y+z=(a^2+a+1)/(a+2)
Now subtract this from your equations.

Answer 3

has 3 fold infinite solution

Answer 4

Ahh thanks.

Answer 5

a= 0 has a single solution