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# math1ZC3_summary.pdf

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School
Department
Mathematics
Course
MATH 1ZC3
Professor
Chris Mc Lean
Semester
Winter

Description
MATH 1ZC3/1B03 - Rough summary of topics covered Elementary Linear Algebra - Applications Version - 10th Edition - Anton and Rorres Matlab Chapter 1: Systems of Linear Equations and Matrices † 1.1 Introduction to Systems of Linear Equations - Augmented matrices and elementary operations † 1.2 Gaussian Elimination - Leading ones, inﬂnite solutions, no solutions, unique solutions † 1.3 Matrices and Matrix Operations - matrix addition, multiplication (order counts!), transpose, trace, linear combination of column vectors † 1.4 Inverses - Properties of inverse, inverse of product, 2x2 inverse, powers † 1.5 Elementary Matrices - ﬂnding the inverse, factoring matrices † 1.6 Systems of Equations and Invertibility - Solving systems Ax = b, start of list of equivalencies † 1.7 Special Matrices - Upper and lower triangular, diagonal, and symmetric matrices Chapter 2: Determinants † 2.1 Cofactor Expansion - Cofactor expansion to ﬂnd determinant † 2.2 Row Reduction eﬁects on the determinant † 2.3 Properties of Determinants - Determinant of a product, adjoint. Cramer’s rule will not be examined Chapter 5: Eigenvalues and Eigenvectors † 5.1 Eigenvalues and Eigenvectors - WHAT IS AN EIGENVECTOR? Ax = ‚x † 5.2 Diagonalization - PDP ¡1 , matrices raised to powers, diagonalizability † 4.12 and Online Modules - Dynamical Systems, v = Av , use and role of eigenvectors, k t+1 t b1‚ 1 1 :::, steady state Appendix B: Complex Numbers Better - 9th Edition Chapter 10, Online modules The 9th edition is available online on Avenue. † 9th ed. 10.1 Complex numbers - complex plane, addition, subtraction, multiplication of rectangular complex numbers † 9th ed. 10.2 More complex numbers - Complex conjugate, modulus of a complex number (absolute value), division by a + bi † 9th ed. 10.3 Polar form - magnitude r, argument µ, conversion between forms, non-unique representation, products and quotients, the n nth roots of a number, e iµ = cosµ + isinµ 1 Chapter 3: Vectors in 2-Space and 3-Space † 3.1 Vectors - sum, diﬁerence, components, scalar multiplication, arithmetic † 3.2 Norm, dot product, and Distance - vector length and distance between points, dot product two ways
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