math: how can I know it is in reduced form

2008-12-14 4:45 pm
Hi anyone,
I was wondering how can I know it is in reduced form. Thank you very much!

True or False

The matrix--1---0---0---0---0---5
---------------0---0---0---0----1--4-----is in reduced form
---------------0---0---0---1----0--4

Thank you very much!

回答 (2)

2008-12-15 4:11 am
✔ 最佳答案
In linear algebra a matrix is in row echelon form if

All nonzero rows are above any rows of all zeroes, and
The leading coefficient of a row is always strictly to the right of the leading coefficient of the row above it.
This is the definition used in this article, but some texts add a third condition:

The leading coefficient of each nonzero row is one.[1]
A matrix is in reduced row echelon form (also called row canonical form) if it satisfies the above three conditions, and if, in addition

Every leading coefficient is the only nonzero entry in its column.
The first non-zero entry in each row is called a pivot.
So according to the definition, the matrix given by you is not in reduced form since the "1" in the third row is on the left hand side of the second row
2008-12-14 7:45 pm
reduced form means the two matrix had done a reduction,
you haven't any comparing is difficulf to know.
Are there any other hints or more question information?


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