Solution to Linear Algebra Hoffman & Kunze Chapter 1.3 Exercise 1.3.5
Solution: Call the first matrix and the second matrix . The matrix is row-equivalent to and the matrix is row-equivalent to
By Theorem 3 page 7 and have the same solutions. Similarly and have the same solutions. Now if and are row-equivalent then and are row equivalent. Thus if and are row equivalent then and must have the same solutions. But has infinitely many solutions and has only the trivial solution . Thus and cannot be row-equivalent.