Consider the set of vectors in the real vector space R3

1 0 1

3 1 p

3 -p -1

For what value(s) p is the set of vectors linearly independent?

Ok, so. I think I'm on the right path.

For A set of vectors to be Linearly independent, the determinent cannot = 0

So i found the Det of that matrix to be p^2 - 3p - 4 and got that p cannot equal 4, or -1. Because that would make the det = zero.

So is he answer all real numbers besides 4 and - 1?