Lecture 4: Square systems and equations of planes.
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Lesson Description:
Learn how to find equations for planes and determine if and where planes intersect each other using matrices.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 15, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.
Additional Resources:
- Lecture Notes - Lecture Notes from this lesson.
- Transcript of Lesson - Written transcript from this lesson.
- Problem Set - A problem set with some problems from this lecture.
Questions answered by this video:
- What are square systems?
- How do you write an equation of a plane through a point given a normal vector??
- How can you determine if two vectors are parallel or perpendicular?
- How can you determine if a vector is parallel or perpendicular to a plane?
- How can you solve a 3x3 linear system?
- How can you find where three planes intersect?
- How do you find the inverse of a matrix?
- When does a matrix have an inverse?
- What are square systems?
- How do you write an equation of a plane through a point given a normal vector??
- How can you determine if two vectors are parallel or perpendicular?
- How can you determine if a vector is parallel or perpendicular to a plane?
- How can you solve a 3x3 linear system?
- How can you find where three planes intersect?
- How do you find the inverse of a matrix?
- When does a matrix have an inverse?
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Staff Review
This video explains some very good examples of finding equations for planes given a point and a normal vector. This is a very practical, useful lecture. Also, you will learn how to find where planes and vectors intersect as well as where two or three planes intersect.
