, which is a model for teaching quantitative fields like engineering and economics: : Moving from elimination to LUcap L cap U factorization. Vector Spaces and Subspaces : Understanding through the lens of column spaces and independent vectors.
When (Ax = b) has no solution, we solve (A^TA\hatx = A^Tb). This minimizes (|Ax - b|^2). The least squares solution is: [ \hatx = (A^TA)^-1A^T b ] lecture notes for linear algebra gilbert strang
The lecture notes are designed to complement Professor Strang's textbooks, which can be found at retailers like Wellesley Publishers (India) MIT OpenCourseWare , which is a model for teaching quantitative