Lesson plan
Elementary matrix
In mathematics, an elementary matrix is a square matrix obtained from the application of a single elementary row operation to the identity matrix. The elementary matrices generate the general linear group when is a field. Left multiplication (pre-multiplication) by an elementary matrix represents the corresponding elementary row operation, while right multiplication (post-multiplication) represents the corresponding elementary column operation. Elementary row operations are used in Gaussian elimination to reduce a matrix to row echelon form. They are also used in Gauss–Jordan elimination to further reduce the matrix to reduced row echelon form.
Article summary
In mathematics, an elementary matrix is a square matrix obtained from the application of a single elementary row operation to the identity matrix. The elementary matrices generate the general linear group when is a field. Left multiplication (pre-multiplication) by an elementary matrix represents the corresponding elementary row operation, while right multiplication (post-multiplication) represents the corresponding elementary column operation. Elementary row operations are used in Gaussian elimination to reduce a matrix to row echelon form. They are also used in Gauss–Jordan elimination to further reduce the matrix to reduced row echelon form.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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