Math 18, Linear Algebra, Spring
2024
Instructors: Eoin Mackall and Andrew Suk
Textbook: Linear Algebra and its Applications (6th Edition), By David C. Lay, Steven R. Lay, and Judi J. McDonald.
Course Description: Matrix algebra, determinants, linear and affine subspaces, Euclidean spaces. Eigenvalues and eigenvectors, quadratic forms, orthogonal matrices. Computing symbolic and graphical solutions using MATLAB.
Syllabus: here (please read carefully).
Website: Canvas
Mylab Homework: Due every Thrursday at 11:59pm.
Lecture 1 (Apr 1) Introducion, systems of linear equations.
Lecture 2 (Apr 3) Row reduction and echelon forms.
Lecture 3 (Apr 5) Vector equations.
Lecture 4 (Apr 8) The Matrix Equation Ax = b.
Lecture 5 (Apr 10) Solution sets of linear systems.
Lecture 6 (Apr 12) Linear independence.
Lecture 7 (Apr 15) Introduction to linear transformations.
Lecture 8 (Apr 17) The matrix of a linear transformation. Matlab HW 1 due
Lecture 9 (Apr 19) Matrix operations.
Lecture 10 (Apr 22) The inverse of a matrix.
Lecture 11 (Apr 24) Characterizations of invertible matrices.
Lecture 12 (Apr 26) Vector spaces and subspaces.
Lecture 13 (Apr 29) Null spaces, column spaces, and linear transformations.
Lecture 14 (May 1) Linearly independent sets; bases. Matlab HW 2 due
Lecture 15 (May 3) The dimension of a vector space.
Lecture 16 (May 6) Coordinate systems.
Lecture 17 (May 8) Introduction to determinants.
Lecture 18 (May 10) Properties of determinants.
Lecture 19 (May 12) Cramer's rule, volume, and linear transformations.
Lecture 20 (May 15) Eigenvectors and Eigenvalues. Matlab HW 3 due
Lecture 21 (May 17) The characteristic equations.
Lecture 22 (May 19) Diagonalization.
Lecture 23 (May 22) Inner Product, length, orthogonality.
Lecture 24 (May 24) Inner product spaces.
Lecture 25 (May 26) No lecture (Holiday).
Lecture 26 (May 29) Orthogonal sets. Matlab HW 4 due
Lecture 27 (May 31) Orthogonal projections.
Lecture 28 (Jun 3) The Gram-Schmidt process.
Lecture 29 (Jun 5) Diagonalization of symmetric matrices. Matlab HW 5 due
Lecture 30 (Jun 7) Review.
Final Exam (Jun 8) 3-6pm. Location TBD.