Question: Let A Rmn, B Rnr, and C = AB. Show that (a) If the column vectors of B are linearly dependent, then the

Let A ∊ Rm×n, B ∊ Rn×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.

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a If the column vectors of B are linearly dependent then Bx 0 for some nonzero vector x R r Thus C... View full answer

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