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i was wondering if anyone could help me with this question:

For what values of a and b does the system

ax +bz = 2

ax +ay +4z = 4

ay + 2z = b

have: (i) no solution

(ii) a unique solution

(iii) a one-parameter solution

(iv) a two-parameter solution?

this is what i did, i wrote it in a matrix form and i did gussian elimination, and across the diagonal i got a, a, and 1

i multiplied the digits on he main diagonal and i got a^2, i made that equal to 0... then i made this post

(basically i'm just doing random things with the numbers and i'm so stuck i don't know what to do! )

any tips would be really appreciated

cheers in advance!

(tomorrow is christmas )