Linear Algebra I

This is a core course for mathematics students and a suitable elective for engineering students. This course provides a grounding on vectors, matrices, and solving systems of linear equations that is fundamental for future mathematics courses and also many practical applications. The course begins by introducing vectors and matrices, and basic operations on them. We then move into the fundamental topic of solving system of linear equations and learn the Gaussian elimination algorithm, an idea that pervades the entire course. In the second half of the course we revisit these ideas in a more abstract way, learning about general vector spaces, linear independence, and the fundamental subspaces associated with a matrix. These ideas are then applied to finding the least squares solution to an inconsistent system of linear equations.