Originally Posted by

**Jhevon** Ok, by determinant of a set of n vectors I assume you mean the determinant of the matrix you get when you use these vectors as rows or columns. in that case, here is the explanation. I'll make it concise, so ask questions if something is not clear.

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actually, it after typing out huge chunks of code, it became apparent to me that MHF is currently having issues with LaTeX. So I'll just tell you how to see it for yourself with hints and directions.

What does it mean for a set of vectors to be linearly dependent? (Hint: your answer should involve an equation and a set of solutions for that equation)

Set this equation up for your set of vectors. Create a system of equations from it, and augment the system into matrices. The matrix to the far left should be the matrix of your vectors.

Now, assume that the determinant of this matrix is zero. This is equivalent to several things. (1) it means the matrix does NOT reduce to the identity, (2) it is not invertible and (3), perhaps the most important here, is that the system won't have a unique solution. It will have many. Now consider what this means based on the first question I asked you