Hey so I have a question about a topic in my Numerical Analysis class (Civil engineering major). Here it is,

1.Give all possible values of A and B for the following system of equations to have the following types of solutions or no solution. If it is not possible then circle "not possible".

a.) Non trivial unique solution

b.) Only trivial solution

c.) Multiple solutions

d.) No solution

x+2y+3z=A

2x+4y+4z=0

Bx+8y+8z=0

I know that if the determinate of the matrix form of these equations is 0 then I have no solution but thats really all I know and I don't know where to start

any help would be appreciated, this is the one topic im confused on for my test this friday and my book does not include help on this topic.