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

Problem:

$\displaystyle S = {(t,1,1), (1,t,1), (1,1,t)} $

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:

$\displaystyle \left(\begin{array}{cccc}t&1&1&0\\1&t&1&0\\1&1&t&0 \end{array}\right)$

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