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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 Carbondale(Date of Approval)AN ABSTRACT OF THE DISSERTATION OFNAME OF STUDENT, for the Doctor of Philosophy degree in MAJORFIELD, presented on DATE OF DEFENSE, at Southern Illinois University Car-bondale.
Theorem 1.3.1. If A is an invertible n×n matrix, then for each n×1 matrix B, the system of equations AX = B has exactly one solution, namely, X = A−1B. Proof. Since A(A−1B) = B, X = A−1B is a solution of AX = B. To show that this is the only solution, we will assume that X0 is an arbitrary solution, and then show
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