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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