Titlebook: Linear Algebra Through Geometry; Thomas Banchoff,John Wermer Textbook 19831st edition Springer-Verlag New York, Inc. 1983 Abstract algebra

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Linear Transformations and Matrices,In Chapter 2.1, we looked at a number of transformations of the plane. Let us list the results we obtained for each transformation ., giving x′ y′, where ..

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EXPEL

Inverses and Systems of Equations,If . are numbers, then .If . is a linear transformation and . and . are vectors, then by Theorem 2.1 of Chapter 2.2

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Cardioplegia

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Differential Systems,.. We are given two tanks of capacity 100 gallons, each filled with a mixture of salt and water. The tanks are connected by pipes as shown in Fig. 2.52 and at all times the mixture in each tank is kept uniform by stirring.

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Vector Geometry in 3-Space,Just as in the plane, we may use vectors to express the analytic geometry of 3-dimensional space.

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Linear Transformations and Matrices,In Chapter 3.1 we examined a number of transformations . of 3-space, all of which have the property that, in terms of the coordinates of . =., the coordinates of T(X) are given by . of these coordinates. In each case the formulae are of the following type:

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