Hey guys,

I have to solve the following problem:

Let the following systems of equations be given:

i)

2x 1 − 3x 2 + x 3 = 4

x 1 − 4x 2 − x 3 = 2

− 3x 1 + tx 2 − 2x 3 = − 3

ii)

x 2 − x 3 = 2

− x 1 + 2x 2 − 4x 3 = 3

x 1 − x 2 + 3x 3 = t + 1

For which values of t does the system have

a) a unique solution? Find this solution.

b) inﬁnitely many solutions? Find the solution set.

c) no solution?

So I started with the first one and get

x2 = -7/(8+t)

so I guess c) if t=8 the system has no solution.

For the others I just don't know how to proceed... Thanks for any help. :)