Prove that if B is a 3 x 1 matrix and C is a 1 x 3 matrix, then the 3x 3 matrix BC has
Chapter 3, Problem 17(choose chapter or problem)
Prove that if B is a \(3 \times 1\) matrix and C is a \(1 \times 3\) matrix, then the \(3 \times 3\) matrix BC has rank at most 1. Conversely, show that if A is any \(3 \times 3\) matrix having rank 1, then there exist a \(3 \times 1\) matrix B and a \(1 \times 3\) matrix C such that A = BC.
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