HackerLec 1 | MIT 18.06 Linear Algebra, Spring 2005
MIT OpenCourseWareYouTube ↗
Further reading 2
What does a matrix do, and which outputs can disappear? →Read a column as an arrow, then a matrix as an action on that arrow. Solving an equation becomes a question about reachable targets, giving collapse, eigenvectors and rotations a geometric interpretation.This video helps answer · What is the same in a diagram and a column calculation?What becomes visible when you change representation? →An average, a spectrum and a geometric diagram each foreground a different structure. Before asking which view is intuitive, ask which comparison you need it to support.This video helps answer · Can changing representation reveal a solution?
Caption notes
Read Ax=b as intersections of constraints or as combinations of matrix columns. Dependent columns leave some targets unreachable.
Original passages · 5
A times x is a combination
of the columns of A.If these three columns
all lie in the same plane, then their combinations
will lie in that same plane.this row picture is getting a little hard to see.the most fundamental operation in the whole courselinear combinations of the columns fill three dimensional space