2.1 Vectors and Linear Combinations
You may have met vectors in physics class, in statics, or in calc 3. In this section we will discuss properties of vectors and begin exploring the connection between vectors and systems of linear equations.
Video
Watch the following video, from 3Blue1Brown which introduces three different ways in which we can understand vectors.
Reading
Then read Chapter 2 Section 1 in Understanding Linear Algebra, by David Austin, and complete Preview Activity 2.1.1.
Here we discuss linear combinations.
Definition: The linear combination of the vectors with scalars is the vector The scalars are called the weights of the linear combination.
In this video we connect expressing a linear combination of a set of vectors to a system of linear equations.
In this video we connect expressing a linear combination of a set of vectors to a system of linear equations.
In this video we look at expressing a vector as a linear combination of vectors using geometry.
Activity
In class we will work on the Magic Carpet Ride Problem (created by the IOLA Team. For more information, visit http://iola.math.vt.edu/index.php)
