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 + 8-𝛌 = 6-𝛍
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?