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Computing

Algebra and Equivalent

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ELEMENTARY LINEAR ALGEBRA K. R. MATTHEWS DEPARTMENT OF MATHEMATICS UNIVERSITY OF QUEENSLAND Corrected Version, 10th February 2010 Comments to the author at [email protected] Contents 1 LINEAR EQUATIONS 1 1.1 Introduction to linear equations . . . . . . . . . . . . . . . . . 1 1.2 Solving linear equations . . . . . . . . . . . . . . . . . . . . . 5 1.3 The Gauss?Jordan algorithm . . . . . . . . . . . . . . . . . . 8 1.4 Systematic solution of linear systems. . . . . . . . . . . . . . 9 1.5 Homogeneous systems . . . . . . . . . . . . . . . . . . . . . . 16 1.6 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2 MATRICES 23 2.1 Matrix arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . 23

unit 4 ch.10, 12, 13

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Instructional Aide / Paraprofessional Test A test for Instructional Aides - Paraprofessionals was developed by CODESP to assist member districts in complying with the testing option requirement of the No Child Left Behind Act of 2001. Test questions were developed by reviewing current and comprehensive job analysis for Instructional Aides, California high school graduation standards, community college placement exams, and other standardized tests currently administered in California. Recommendations from subject matter experts were also valuable in this process. Ability to Assist in Instruction test questions are also included with the sample test. Members have two choices, they can use a pre-assembled test which

AP Euro Notes

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Building an Essential World History Tool: Teaching Comparative History Comparison may be the most widely used demonstration of higher level thinking in history courses. Teachers usually assume students can compare because everyone makes comparisons so often. Yet frequency of activity does not guarantee the quality. The value of comparative history: Comparison locates the distinctive Comparison locates the common Comparison locates hidden elements in a situation ? applying what is obvious in one situation to another or asking questions raised in one place of another can reveal hidden attributes. Comparative history stimulates students to use higher-level thinking skills. Thinking the comparative method:

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