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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 2 Vocabulary

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Unit Two: 1775-1825 War for Independence With the Declaration of Independence as its fuel, America entered a war for independence with Great Britain: the Revolutionary War. Throughout the war, America developed its first real feelings of nationalism and ended up being victorious in its fight for freedom. Advantages/Disadvantages for Britain: The British were well equipped, well trained, and well disciplined. They had a strong navy to land troops, transport troops, guard communication and supply lines. Also, they had a large sum of money which could be used to hire foreign mercenaries. However, they were outnumbered by the U.S. Advantages/Disadvantages for U.S.: Many colonists knew how to use firearms. They

AP US History Ch 27 Notes

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Book: American Pageant, Ch. 27, Imperialism and Big Stick Policy There's a bit of shorthand, but most of it should be pretty clear if you've at least skimmed the chapter. Imperialist: The policy of the US toward other nations in the late 1800s, characterized by the takeover of Latin American countries in order to gain access to their resources. Pulitzer and Hearst: Famous for their 'yellow journalism', in which insane exaggerated, fabricated stories drove the public toward imperialism and war with foreign nations. Aggressive. Darwinism: The earth belongs to the strong and fit. <-- According to Teddy Roosevelt and Henry Cabot Lodge. Larger nations have the obligation and right to dominate smaller ones, and to use them for all their worth.

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