Friday 11th September: Rules for vectors: equality, addition, scalar multiplication, subtraction (3.1). The norm of a vector; distance between two points in Rn (3.2).
Wednesday 16th September (shortened class due to fire alarm): Equation of a line in R2; normal vectors; orthogonal projections (3.3).
Friday 18th September: Distance from a point to a line; lines in R3, parametric equations (3.5).
Wednesday 23rd September: Planes in R3: equations in point-normal form and general form, examples; lines and planes in R3 (3.5).
Friday 25th September: Intersection of lines and planes in R3; distance from a point to a plane in R3; distance from a point to a line in R3; intersection of two and three planes in R3 (all 3.5).
Wednesday 30th September: Finding solutions to systems of linear equations: the augmented matrix of a linear system; elementary row operations (1.1).
Friday 2nd October: Row-echelon form and reduced row-echelon form (RREF) of a matrix; using RREF to solve linear systems; examples with unique solution, infinitely many solutions, no solutions (1.2).
Wednesday 7th October: Introduction to vector spaces: definition and examples (5.1).
Friday 9th October: More on vector spaces: closure under addition and scalar multiplication; more examples/non-examples (5.1).
Wednesday 14th October: Subspaces; the Subspace Test; examples (all 5.2).
Friday 16th October: TEST 1.
Wednesday 21st October: Properties of the span, including that the span is a subspace; spanning sets: definition and examples (all 5.2).
Friday 23rd October: Linearly independent and linearly dependent sets of vectors: definition and examples (5.3).
Wednesday 28th October: Bases for subpaces; the dimension of a vector space: definition and examples (all 5.4).
Friday 30th October: Orthogonal and orthonormal bases; the Gram–Schmidt Process (6.3: note that the treatment given by the textbook is much more advanced that what we did).
Wednesday 4th November: Matrices; notation for matrices; operations on matrices: addition, subtraction, scalar multiplication, matrix multiplication (all 1.3).
Friday 6th November: The zero matrix and identity matrix; row and column matrices; row space and column space of a matrix; matrix form of a linear system; null space (1.3, 1.4, 5.5).
Wednesday 11th November: NO CLASS (due to Remembrance Day).
Friday 13th November: TEST 2.
Wednesday 18th November: Examples of computing the inverse (1.5); matrix powers, negative powers, laws of exponents, matrix polynomials (1.4).
Friday 20th November: Review of Test 2; determinants, cofactor expansion (2.1).
Wednesday 25th November: Determinants of: invertible matrices, elementary matrices, products of matrices, inverses, sums and transposes (2.2/2.3).
Friday 27th November: Finding bases for the row space, column space and null space of a matrix (5.5). Linear transformations: definition and examples (4.2/4.3).
Wednesday 2nd December: Rotations and reflections as linear transformations in R2 (4.2); composition of linear transformations and matrix multiplication (4.2); one-to-one linear transformations (4.3).
Friday 4th December: Eigenvalues and eigenvectors of linear transformations and matrices; finding eigenvalues by solving the characteristic equation; eigenspaces and finding bases for eigenspaces (all 7.1; also mentioned briefly in 2.3 and 4.3).
Wednesday 9th December: Review class.
Page last updated: 7th December 2009.
Back to course homepage