Let A ∈ Rm×n, B ∈ Rn×r , and C = AB. Show that (a) if the column vectors of B are l...

Let A ∈ R^m×n, B ∈ R^n×r , and C = AB. Show that

(a) if the column vectors of B are linearly dependent, then the column vectors of C must be linearly dependent.

(b) if the row vectors of A are linearly dependent, then the row vectors of C are linearly dependent.

[Hint: Apply part (a) to C^T.]