
Matricies
The variables x, y, z satisfy the equations
x + 2y + 3y = 2
x + 3y + 2z = 1
2x + 2y + 𝛌z = 𝛍
where, 𝛌, 𝛍 are constants
a) using reduction to echelon form, or otherwise,
i) Find the value of 𝛌 for which these equations do not have a unique solution
ii) for this value of 𝛌, find the value of 𝛍 for which the equations are consistent.
b) for your values of 𝛌,𝛍, find the general solution of these equations.
I have managed to reduce the equations to
x + 2y + 3z = 2
0  y + z = 1
0 + 0 + 8𝛌 = 6𝛍
I'm not sure what to do next as i'm not sure what it means 'or which these equations do not have a unique solution'
Has anybody got any ideas?
thanks

Hello, djmccabie!
Couldn't you use letters for the constants?
Quote:
a) Using reduction to echelon form, or otherwise,
i) Find the value of for which these equations do not have a unique solution.
We have: .
. .
If , the system does not have a unique solution.
Quote:
ii) For this value of , find the value of for which the equations are consistent.
If , then produces a system with an infinite number of solutions.
(If , the system has no solution.)
Quote:
b) For your values of , find the general solution of these equations.
If and , then [3] becomes: .
And we have: .
. . which can be written: .
On the right, replace with a parameter
This represents all the solutions to this system of equations.