Question

Is the set {(2,0,0),(3,4,0),(200,567,0)} linearly independent?

Answer 1

If the determinant of the matrix is not zero, the system is linearly independent.

Answer 2

there are about 10 other ways to show it, but this is one...
also you can reduce it to the identity matrix using gauss-jordan is yet another way

Answer 3

yup

Answer 4

countless ways