Using determinant for linear dependence

[periphrasticobfuscation]

Hi all,

Does anyone know whether we can use the determinant to find whether 3 vectors in R^3 are linearly independent/dependent in Exam 1?

Our Maths teacher says we probably shouldn't because it's not in the study design, but I don't understand why we have to take the long way around. I honestly thought the whole point was to find the quickest and most efficient way to solve problems

Thanks all!

[S_R_K]

It is a valid method and will be (and has been) accepted on end of year exams.