Transposes, Permutations, Vector Spaces

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Session Overview

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

To account for row exchanges in Gaussian elimination, we include a permutation matrix P in the factorization PA = LU. Then we learn about vector spaces and subspaces; these are central to linear algebra.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 2.7 in the textbook.

Problem Solving Video

  • Watch the recitation video on Subspaces of Three Dimensional Space (00:14:44)
  • Recitation video transcript (PDF)
  • 观看视频: 习题讲解 -- 三维空间的子空间 (00:13:07) [watch this recitation in Mandarin]

Check Yourself

Problems and Solutions

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


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