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 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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