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Suppose R and R0 are 2 ⇥ 3 row-reduced echelon matrices and that the systems RX...

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Advance Math

Suppose R and R0 are 2 ⇥ 3 row-reduced echelon matrices and thatthe systems RX = 0
andR’X = 0 have exactly the same solutions. Prove that R = R’
.

Answer & Explanation Solved by verified expert
3.8 Ratings (648 Votes)
The main idea is to prove that each row of each matrix is a linear combination of the rows of the other matrix First suppose that one of the matrices R R has one zero row Then the solutions of the corresponding system depend on 2 parameters Hence the other matrix also has a zero row and the second rows of R R coincide they are both zero    See Answer
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