Systems of equations, matrices, vectors, and geometry
Instructed by Hania Uscka-Wehlou 46 hours on-demand video & 361 downloadable resources
What you’ll learn
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How to solve problems in linear algebra and geometry (illustrated with 175 solved problems) and why these methods work.
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Solve systems of linear equations with help of Gauss-Jordan or Gaussian elimination, the latter followed by back-substitution.
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Interpret geometrically solution sets of systems of linear equations by analysing their RREF matrix (row equivalent with the augmented matrix of the system).
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Matrix operations (addition, scaling, multiplication), how they are defined, how they are applied, and what computational rules hold for them.
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Matrix inverse: determine whether a matrix is invertible; compute its inverse: both with (Jacobi) algorithm and by the explicit formula; matrix equations.
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Determinants, their definition, properties, and different ways of computing them; determinant equations; Cramer’s rule for n-by-n systems of equations.
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Vectors, their coordinates and norm; geometrical vectors and abstract vectors, their addition and scaling: arithmetically and geometrically (in 2D and 3D).
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Vector products (scaling, dot product, cross product, scalar triple product), their properties and applications; orthogonal projection and vector decomposition.
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Analytical geometry in the 3-space: different ways of describing lines and planes, with applications in problem solving.
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Compute distances between points, planes and lines in the 3-space, both by using orthogonal projections and by geometrical reasoning.
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Determine whether lines and planes are parallel, and compute the angles between them (using dot product and directional or normal vectors) if they intersect.
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How to geometrically interpret n-by-2 and n-by-3 systems of equations and their solution sets as intersection sets between lines in 2D or planes in 3D.
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Understand the connection between systems of linear equations and matrix multiplication.
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Invertible Matrix Theorem and its applications; apply determinant test in various situations.
Who this course is for:
- University and college engineering
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