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16: Appendix 1 - Vector and Matrix Math
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16.1: Vectors
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Vector representation in two and three dimensions. Covers magnitude-and-direction form, component form, and conversion between the two forms. Includes several worked examples.
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16.2: Vector Addition
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Adding vectors in two and three dimensions, through the geometric addition and component addition methods.
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16.3: Dot Product
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The dot product (also sometimes called the scalar product) is a mathematical operation that can be performed on any two vectors with the same number of elements. The result is a scalar number equal to the magnitude of the first vector, times the magnitude of the second vector, times the cosine of the angle between the two vectors.
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16.4: Cross Product
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The cross product is a mathematical operation that can be performed on any two three-dimensional vectors. The result of the cross product operation will be a third vector that is perpendicular to both of the original vectors and has a magnitude of the first vector times the magnitude of the second vector times the sine of the angle between the vectors.
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16.5: Solving Systems of Equations with Matrices
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Converting a system of linear equations into a matrix, to be solved by computer. Includes worked example.
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16.6: Appendix 1 Homework Problems
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