Show that this system does not have a unique solution for any value of $\lambda$ .

(i)     Determine the value of $\lambda$ for which the system is consistent.

(ii)     For this value of $\lambda$ , find the general solution of the system.

using row operations,     M1

to obtain 2 equations in the same 2 variables     A1A1

for example $y - z = 1$

$2y - 2z = \lambda  - 1$

the fact that one of the left hand sides is a multiple of the other left hand side indicates that the equations do not have a unique solution, or equivalent     R1AG

[4 marks]

(i)     $\lambda = 3$     A1

(ii)     put $z = \mu$     M1

then $y = 1 + \mu$     A1

and $x = - 2\mu$ or equivalent     A1

[4 marks]