Independent columns: Ax = 0 has one solution. A is an invertible matrix.
Dependent columns: Cx = 0 has many solutions. C is a singular matrix.
These statements are from Gil's LA. The full context is here:https://imgur.com/a/BSTRDpB
Can this be explained in greater detail? Why is it that when a matrix has independent columns, it is invertible? Is it a fact I should simply take at face value?