Conflicting definitions of linear independence

[PeroK]

Thank you. To avoid confusion, I should have posted the matrix I was using, but for some reason when I post LaTeX code with my computer on this website, I only see the code, not the "finished product."

You have to keep refreshing the page.

I was not putting the three vectors into a 4x4 matrix, but rather into a 3x4 matrix.

The vectors should be columns in your matrix. It doesn't work if you make the vectors the rows. You should check this yourself.