Lecture 34: Introduction to range of a linear transformation, column space of a matrix (Nicholson Section 5.4)
Sub Project: Linear Algebra Lecture Videos
Alternate Video Access via MyMedia | Video Duration: 50:55
Description: L is a linear transformation from R^n to R^m and A is a mxn matrix. Started with a review of Null(L) and the solution space of Ax=0; these are subspaces of R^n.
2:00 --- introduced the range of a linear transformation and the column space of a matrix. These are subspaces of R^m.
5:30 --- Found Range(L) where L is the linear transformation corresponding to projection onto a specific vector. Once we found Range(L), then we found a basis for Range(L).
21:30 --- Found Range(L) where L is the linear transformation corresponding to projection onto a specific plane. Once we found Range(L), then we found a basis for Range(L).
37:55 --- Defined the column space of a matrix: Col(A).
39:10 --- given a specific matrix, A, found a basis for Col(A).
