18.06SC | Fall 2011 | Undergraduate

Linear Algebra

Unit II: Least Squares, Determinants and Eigenvalues

Orthogonal Vectors and Subspaces

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Session Overview

Figure excerpted from 'Introduction to Linear Algebra' by G.S. Strang

Vectors are easier to understand when they’re described in terms of orthogonal bases. In addition, the Four Fundamental Subspaces are orthogonal to each other in pairs.

If A is a rectangular matrix, Ax = b is often unsolvable. The matrix ATA will help us find a vector x̂ that comes as close as possible to solving Ax = b.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 4.1 in the 4th or 5th edition.

Problem Solving Video

Check Yourself

Problems and Solutions

Work the problems on your own and check your answers when you’re done.

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Course Info

Departments
As Taught In
Fall 2011
Learning Resource Types
Lecture Videos
Exams with Solutions
Lecture Notes
Recitation Videos
Problem Sets with Solutions
Simulations
Course Introduction
Instructor Insights