# An algebra problem by Hobart Pao

Algebra Level 3

Given column vector $$A \in \mathbb{R}^n$$ and row vector $$B \in \mathbb{R}^n$$, if column vector A in rewritten as row vector B, such that entries $$A_{n1}$$ in matrix A become entries $$B_{1n}$$ in matrix B, where $$n \in \mathbb{N}$$, then which of the following statements are necessarily correct?

1. If vector A has a rank of 1, then vector B also has a rank of 1.

2. If vector A is in reduced row-echelon form, then vector B will also be in reduced row-echelon form.

×