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If A is a 3 x 5 matrix, then the number of leading 1’s in its reduced row echelon form is at most _____. Explain your solution.

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closed as off-topic by Belgi, Grigory M, Thursday, amWhy, Hans Engler Jun 14 at 15:21

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have you tried anything ? –  Dominic Michaelis Feb 19 '13 at 23:15
Seriously?............. –  gnometorule Feb 19 '13 at 23:15
Really?........... –  user60610 Feb 19 '13 at 23:18
I want to say 3 but I'm not sure how to explain myself. –  shaya Feb 19 '13 at 23:21
try to explain it –  Dominic Michaelis Feb 19 '13 at 23:23

2 Answers 2

up vote 2 down vote accepted

There is at most one such $1$ per row. There are $3$ rows. So it is at most $3$.

Moreover, you can easily construct an example where it is exactly $3$, so $3$ is sharp.

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row-echelon form states that every row starts with a 1. so if you have 3 rows, that means you have at most 3 leading 1's. There is your answer.

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