A major application of linear algebra is to solving systems of linear equations. This lecture presents three ways of thinking about these systems. The "row method" focuses on the individual equations, the "column method" focuses on combining the columns, and the "matrix method" is an even more compact and powerful way of describing systems of linear equations.
Portion of Fig. 2.2 from the textbook Introduction to Linear Algebra.
Lecture Video and Summary
- Watch the video lecture The Geometry of Linear Equations (00:39:49)
The Geometry of Linear Equations
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 1.1, 1.2, and 2.1 in the 4th or 5th edition.
Problem Solving Video
- Watch the recitation video on Geometry of Linear Algebra (00:16:35)
Geometry of Linear Algebra
- Recitation video transcript (PDF)
- 观看视频: 习题讲解 -- 线性代数的几何表示 (00:15:34)[watch this recitation in Mandarin]
Problems and Solutions
Work the problems on your own and check your answers when you're done.