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Difference between Normal Form and Echelon Form

Difference between Normal Form and Echelon Form

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What makes the normal form of a matrix legally valid?

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Instructions and help about echelon and normal form of a matrix

In this video, we're going to review the machinery of row reduction and how we turn a general matrix into a matrix in row-echelon form, which is good, and reduced row-echelon form, which is best. So the rules of the game are that if somebody gives you a matrix, a row operation is something that you do where you can rescale a row, that is multiply a row by any non-zero constant, or you can add a multiple of one row to another row or you can swap two rows. These are called row operations. The goal is that somebody gives you a matrix, you want to apply a bunch of row operations until the matrix either becomes in row-echelon form or reduced row-echelon form. What row-echelon form means is that some of the rows might be nothing but 0's. If you have a row that is nothing but 0's, it has to be at the very bottom of the matrix. Every other row has a first non-zero entry. The first non-zero entry is called a pivot. This is a pivot, this is a pivot, this is a pivot, this

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