Lecture 33: Introduction to Solution space, Null space, Solution set (Nicholson Section 5.4)
Sub Project: Linear Algebra Lecture Videos
Video Link: Lecture 33: Introduction to Solution space, Null space, Solution set (Nicholson Section 5.4)
Alternate Video Access via MyMedia | Video Duration: 48:37
Description: Lecture starts at 1:26. Given a matrix A, defined the “solution space of Ax=0” and, given a linear transformation L from R^n to R^m, defined Null(L).
6:20 --- proved that Null(L) is a subspace of R^n.
16:00 --- example of L:R^3 → R^3 where L corresponds to projection onto a specific vector. Found Null(L) by geometric/intuitive arguments. Verified the intuition by representing the linear transformation as a matrix transformation and finding the corresponding solution space. Found a basis for Null(L). Found the dimension of Null(L).
31:45 --- example of L:R^3→R^3 where L corresponds to projection onto a specific plane. Found Null(L) by geometric/intuitive arguments. Verified the intuition by representing the linear transformation as a matrix transformation and finding the corresponding solution space. Found a basis for Null(L). Found the dimension of Null(L).
41:45 --- Given an mxn matrix A, defined the solution set of the system Ax=b. Found solution set for a specific 2x4 matrix A. This is an important example because A has a column of zeros and students often get confused by such matrices! Wrote the solution set as a specific solution of Ax=b plus a linear combination of solutions to the homogeneous problem Ax=0.
