Verified Documents at Queen's University

MATH 112 Lecture 1: linear algebra, applications, linear equation, examples, linear system, solution set, consistency, introduction to matrices

MATH 112 Lecture 2: Elementary row operations, row equivalency, example problems, leading entry, zero/nonzero row, row echelon form, reduced row echelon form, pivot positions and columns, row reduction, theorem

MATH 112 Lecture 3: solving linear systems with reduced row echelon form, basic and free variables, existence and uniqueness theorem, examples, summary

MATH 112 Lecture Notes - Lecture 4: Root Mean Square, Scalar Multiplication

MATH 112 Lecture 5: Practise span, problems, matrix-vector product Ax, row-column rule

MATH 112 Lecture 5: Week 2

MATH 112 Lecture 6: Week 2

MATH 112 Lecture 6: Solution set matrix theorem, equivalent statements matrix theorem, solution sets of linear systems (homogeneous and inhomogeneous, parametric vector form), practice problems

MATH 112 Lecture 7: Week 3

MATH 112 Lecture Notes - Lecture 7: Indep, Linear Combination

MATH 112 Lecture Notes - Lecture 8: Linear Map

MATH 112 Lecture 9: Linear transformation theorem, practice problems, mapping, finding the standard matrix of a linear transformation, reflections, rotations

MATH 112 Lecture Notes - Lecture 10: Linear Map

MATH 112 Lecture 11: Matrix algebra, square matrix, identity matrix, zero matrix, properties, examples, matrix product, theorems

MATH 112 Lecture 12: Row-column rule, properties of matrix product, warning, example, powers of a matrix, matrix transpose, matrix transpose properties

MATH 112 Lecture 13: Matrix tranpose, symmetric matrix, matrix transpose properties, scalar (dot) product, matrix inverse, inverse of a 2*2 matrix

MATH 112 Lecture 15: Theorem, proof, solving linear systems with the inverse of a matrix, properties of the inverse, when a square matrix is invertible, elementary matrix, invertible matrix theorem

MATH 112 Lecture 16: Invertible 2x2 and 3x3 matrices, determinants, theorem, practice problems with cofactor expansion

MATH 112 Lecture 17: triangular matrices, theorem, determinant and elementary row operation, properties of determinant, detA^T = detA theorem

MATH 112 Lecture 18: Induction for larger matrices, determinant and column operations, multiplicative property theorem, elementary matrix theorem, proof

MATH 112 Lecture 22: the inner product, dot product, theorem, proof, length in R^n, solving with Pythagoras, vector length, unit vectors, distance in R^n, orthagonality

MATH 112 Lecture 23: The law of cosines, theorem involving cosines and vectors, orthogonal projection, area and volume problems

MATH 112 Lecture Notes - Lecture 24: Fdisk, Ellipse, Linear Map

MATH 112 Lecture 26: Vector space defined by ten axioms, examples, problems, subspace of a vector space definition

MATH 112 Lecture 27: More examples with vector space, Linear combination and Span definition, examples, maps, kernels, ranges, theorem combining vector space, spans, and subspaces

MATH 112 Lecture 28: kernel r range-recap, linear independence, theorem, practice problems

MATH 112 Lecture 29: Practice with linear independence/dependence, spanning set theorem, b-coordinates, basis, practice problems

MATH 112 Lecture Notes - Lecture 30: Chinese House (Potsdam)

MATH 112 Lecture Notes - Lecture 31: Eigenvalues And Eigenvectors, Weck

MATH 112 Lecture Notes - Lecture 32: Eigenvalues And Eigenvectors

MATH 112 Lecture 33: difference equations, examples of linear difference equations, scalar form of difference equation, general formula for yk

MATH 112 Lecture 34: power of a matrix, definition involving nxn matrices and invertible matrices, theorem, proof

MATH 112 Lecture Notes - Lecture 35: Catalan Shawm

MATH 112 Lecture 36: Continuing previous example with diagonalization, more practice problems

MATH 112 Lecture 37: diagonalization summary, similarity: the change of basis viewpoint, complex numbers, addition and multiplication of complex numbers, practice problems