Linear Algebra in Twenty Five Lectures

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Linear Algebra in Twenty Five LecturesTom Denton and Andrew WaldronMarch 27, 2012Edited by Katrina Glaeser, Rohit Thomas & Travis Scrimshaw1Contents1 What is Linear Algebra ?122 Gaussian Notation for Linear Systems . . . . . . . . . . . . . . . . . . . Reduced Row Echelon Form . . . . . . . . . . . . . . . . . . . 213 Elementary Row Operations274 Solution Sets for Systems of Linear Non-Leading Variables . . . . . . . . . . . . . . . . . . . . . . 355 Vectors in Space, Directions and Magnitudes . . . . . . . . . . . . . . . . . . . . 466 Vector Spaces537 Linear Transformations588 Matrices639 Properties of Block Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . The Algebra of Square Matrices. . . . . . . . . . . . . . . . 7310 Inverse Three Properties of the Inverse.

1 What is Linear Algebra?12 2 Gaussian Elimination19 ... C Sample Final Problems and Solutions231 D Points Vs. Vectors256 E Abstract Concepts258 ... solutions as well as a sample nal exam. There are also a set of ten on-line assignments which are usually collected weekly. The rst …

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