If a set of n vectors in an n-dimensional space is linearly independent, what can be said about the determinant of the matrix they form?
Show answer
It is non-zero
A non-zero determinant indicates that the vectors do not lie in a lower-dimensional subspace. This is equivalent to saying the matrix is invertible and the corresponding linear system has a unique solution.
Also asked as:
- If n vectors in an n-dimensional space are linearly independent, what property must the determinant of the matrix formed by these vectors have?