I am having difficulties with the following problem. I need to find values of t that make the set linearly independent.

Problem:

The answer is all t not equal to 1 and -2. I am confused on how to approach this problem.

If I set up a matrix I believe I see where -2 comes from. And we need t to not equal that otherwise that's another solution to the homogeneous equation. Matrix:

Beyond seeing where those two numbers come from, I am not sure of the procedure behind getting them. Thanks for any help.