
Row equivalent matrix properties - yanman
I have been arguing with two linear algebra professors about the following question.<p>Given function T: R^3 to R^3<p>T(x1, x2, x3) = (2x2 + x3, x1 - 4x2, 3x1 + 6x3)<p>For which of the following triplets (x1, x2, x3) do we have T(x1, x2, x3) = T(1, 1, 1)?<p>A (-2, 1, 4)
B(-3, 0, 3)
C(3, 3&#x2F;2, 0)
D(-6, 0, 6)
E(-1, 1&#x2F;2, 2)
F None of the above<p>This was a problem given on a web platform that was graded upon submission.<p>Professor One stated that this question and another similar question should be disregarded because the &quot;correct&quot; answers are not the answers that the computer regards as correct.<p>When I submitted my answers to these two questions BOTH were marked as correct. So how could I have derived the &quot;wrong&quot; right answers to both questions? By chance? So I provided my methods to Professor one who said my answers couldn&#x27;t be correct because I used the reduced row echelon form matrix and not the original matrix. So I did it again, and got the right answer, then applied it to another row equivalent matrix, and got the right answer again, and so on and so on.<p>My argument is that the resulting T(1, 1, 1) is different for every different row equivalent matrix. But the provided triplets that produce the same results as each T(1, 1, 1) applied to each different, but row equivalent matrix is THE SAME! therefore each version of a row equivalent matrix produces different results, but the triplet transformation that produce the same results as a different transformation to the same matrix are THE SAME FOR EVERY ROW EQUIVALENT MATRIX.<p>Is this not true? How can these professionals not see this. I feel like I&#x27;m in  the Twilight Zone.<p>Why
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gigatexal
maybe try here: [http://math.stackexchange.com](http://math.stackexchange.com)

[http://math.stackexchange.com/questions/674204/two-proofs-
ab...](http://math.stackexchange.com/questions/674204/two-proofs-about-
invertible-matrix-and-row-equivalent-to-the-identity-matrix) <\-- maybe this
helps?

