LINEAR ALGEBRA: nontrivial solutions

[alexis36]

Homework Statement

I am asked to find all the values of "b" for which the following system has a nontrivial (i.e non-zero solution).

Homework Equations

bx1 - bx3 = 0
x1 + (b+1)x2 + 2x3 = 0
bx1 + (2b+2) x2 = 0

The Attempt at a Solution

I know that I am needing to solve for the equations so that I dont' end up with a row of all zeroes.
But I am just confused as to where to start. Because I have a bunch of different variables, and I don't know if I should assign parameters to begin with or not?

 

[Dr Transport]

write as a matrix with x1, x2, and x3 factored out then find the determinant of the result.

 

[alexis36]

thank you!