Determine whether or not the following collection of vectors are linearly independent in R 4 . If it is linearly dependent, state the nature of...

Determine whether or not the following collection of vectors are linearly independent in R 4 . If it is linearly dependent, state the nature of dependence. Then, briefly explain why we know ahead of time that this will not form a basis for R 4 prior to any calculation or outcome.

{ [1 2 -3 1], [3 7 1 -2], [1 3 7 -4] }