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Asked Dec 28, 2019

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Prove that if B is a 3×1 matrix and C is a 1×3 matrix, then the 3×3 matrix BC has rank at most 1. Conversely, show that if A is any 3×3 matrix having rank 1, then there exist a 3 x1 matrix B and a 1 ×3 matrix C such that A = BC.

Step 1

Let A be the 3 × 3 matrix of rank 1, th...

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