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Linear Algebra in Twenty Five Lectures

Linear Algebra in Twenty Five LecturesTom Denton and Andrew WaldronMarch 27, 2012 Edited by Katrina Glaeser, Rohit Thomas & Travis Scrimshaw1 Contents1 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 .. Finding Inverses .. Linear Systems and Inverses .. Homogeneous Systems .. Bit Matrices .. UsingLUDecomposition to Solve Linear Systems.

involving some permutation of the words \linear", \algebra" and \applica-tions"). Instead, they attempt to explain the fundamental concepts carefully enough that students will realize for their own selves when the particular application they encounter in future studies is ripe for a solution via linear algebra.

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