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Unformatted text preview: NOTES ON SECTION 2 . 1 , 2 . 2 MA265, SECTIONS 41, 52 Key words Elimination method Row echelon form Pivot column Reduced row echelon form (RREF) Row operation Pivot Leading one Row equivalent 1. Reduced row echelon form Definition 1. A matrix is in reduced row echelon form if (1) Every row of zeros appears below any nonzero row. (2) The first nonzero entry of any nonzero row is a one, and this entry is called a leading one . (3) Any leading one is the unique nonzero entry in its column. (4) The leading one in row r appears to the right of every leading one that appears on any row above row r . It is perhaps easier to understand in terms of examples of matrices in RREF, for which you can look in the textbook. Definition 2. A matrix is in row echelon form if it satisfies the properties of being in RREF except that it is allowed to fail property (2) . Remark 3. For most applications, the row echelon form of a matrix suffices. However, it is still useful to talk about the RREF for various reasons, some of which are • The algorithm to find the inverse of a matrix requires us to put a certain matrix in RREF (echelon form is not good enough)....
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 Spring '08
 Bens
 Linear Algebra, Algebra, Gaussian Elimination, Row echelon form

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