Question
Consider a set of n vectors in the space R^n.
Why do we say that a n*n matrix with those vectors as it's columns, is a basis for the vector space R^n, if that matrix is invertible?
Why do we say that a n*n matrix with those vectors as it's columns, is a basis for the vector space R^n, if that matrix is invertible?
Answers
oobleck
consider the determinant of the matrix. If the vectors are dependent, it is zero, so it has no inverse.
Ashley
Thank you!