Transposes, Permutations, Vector Spaces

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Session Overview

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

• Watch the video lecture Transposes, Permutations, Vector Spaces (00:47:42)

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  Transposes, Permutations, Vector Spaces

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• Read the accompanying lecture summary (PDF)
• Lecture video transcript (PDF)

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)

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  Subspaces of Three Dimensional Space

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• 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]

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  三维空间的子空间

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Check Yourself

Problems and Solutions

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

• Problems (PDF)
• Solutions (PDF)

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