Hi again, I think I have the correct answer to part a of this question but I I am not sure about part b, so would someone be kind enough to check my working please.

a) solve in for

b) find the number of solutions for

Working:

a)

so it is not invertible for

so I get

For : and so solution for is

For , solution is

For , solution is

b) For p=7 the matrix in not invertible so for the two linear equation one is a scalar of the other.

therefore

Thus, for each choice of , .

So there are 7 possible solutions: