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A SAMPLE RESEARCH PAPER/THESIS/DISSERTATION ON …

A SAMPLE RESEARCH PAPER/THESIS/DISSERTATION ON ASPECTS OFELEMENTARY LINEARY ALGEBRAbyJames , Southern Illinois University, 2010A RESEARCH Paper/ thesis /DissertationSubmitted in Partial Fulfillment of the Requirements for theMaster of Science DegreeDepartment of Mathematicsin the Graduate SchoolSouthern Illinois University CarbondaleJuly, 2006(Please replace Name and Year with your information and delete all instructions)Copyright by NAME, YEARAll Rights Reserved**(This page is optional)** RESEARCH PAPER/THESIS/DISSERTATION APPROVALTITLE (in all caps)By(Author)A thesis /Dissertation Submitted in PartialFulfillment of the Requirementsfor the Degree of(Degree)in the field of (Major)Approved by:(Name of thesis /dissertation chair), Chair(Name of committee member 1)(Name of committee member 2)(Name of committee member 3)(Name of committee member 4)Graduate SchoolSouthern Illinois University

Remark. It is not difficultto see that a matrix in row-echelon form must have zeros below each leading 1. In contrast a matrix in reduced row-echelon form must have zeros above and below each leading 1. As a direct result of Figure 1.1 on page 3 …

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A SAMPLE RESEARCH …

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De nition 1. A matrix is in row echelon form if 1. Nonzero rows appear above the zero rows. 2. In any nonzero row, the rst nonzero entry is a one (called the leading one). 3. The leading one in a nonzero row appears to the left of the leading one in any lower row. 1

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Fundamental Theorem 2: if an matrix can be reduced to row echelon form possibly with row interchanges, then has an -decomposition where is a product of row interchange elementary matrices, is lower triangular with entries on the diagonal and is upper triangular. Fundamental Theorem 2 is the version that's most often used in large scale ...

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Reducing the augmented matrix of this system to row-echelon form, we obtain 1 −24 x1 01−1 −x1 −x2 0007x1 +11x2 +x3 . It follows that the system is consistent if and only if x1, x2, x3 satisfy 7x1 +11x2 +x3 = 0. (4.4.4) Consequently, Equation (4.4.3) holds only for those vectors v = (x1,x2,x3) in R3 whose components satisfy Equation (4.4.4).

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