Let A ∈ Rm×n, B ∈ Rn×r , and C = AB. Show that
(a) if A and B both have linearly independent column vectors, then the column vectors of C will also be linearly independent.
(b) if A and B both have linearly independent row vectors, then the row vectors of C will also be linearly independent. [Hint: Apply part (a) to CT .]
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