Why is this example in row echelon form?

Course Q&A Math for Machine Learning Linear Algebra for Machine Learning and Data Sc...
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Lecture: Matrix row-reduction

At 2 minutes in the lecture, this matrix is described as being in row echelon form because it has 1s in the main diagonal and 0s underneath:

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Why is this matrix shown as being in row echelon form?

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(2 minutes 32 seconds in the video). This does not have 1s in the main diagonal?

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Luis said both are row echelon form which means that being an upper diagonal matrix with 1s in the diagonal is only a sufficient but not a necessary condition.

This wikipedia definition will fit the two cases in your question (and cases of less equations than variables).

Cheers!

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