Need Explination (linear Indpendance)

[stuckie27]

A and B are both Matricies,

Suppose the last column of AB is entirely zero but B itself has no column of zeros. What can be said about the columns of A?

Answer: The columns of A are Linearly Dependant.

Question: Why?

[franznietzsche]

Suppose the last column o AB is entirely zero but B itself has no column of zeros. What can be said about the columns of A?

Answer: The columns of A are Linearly Dependant.

Question: Why?

Are A and B contravariant vecotrs? is AB their inner (scalar) product? If so, i'm not sure how it can have columns, please clarify.

[stuckie27]

edit, A and B are each a different Matrix.

[matt grime]

take a column in AB, what do the entries represent? are they in some way related to linear combinations of the columns of A? (yes they are, that isn't rhetorical) and a column of zeroes might mean that.... fill in the blanks using the definition of linear (in)dependence.