I row reduced to the matrix depicted,(please see attached pic) but apparently its wrong ...
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Your work looks right to me. I also tried reducing it with a CAS, and it also got the same answer.
Why do you think it's wrong?
It is ok if you are allowed to swap rows but not ok if you are not able to. I agree with you that your solution should be the row reduced echelon form since it has the right leading 1's and structure.
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