Vector Algebra

In this video I go over the addition, subtraction, and scalar multiplication of vectors but algebraically. This is done by treating each vector component separately and then applying basic algebraic rules to these components to finally obtain a new vector. I illustrate this by visually graphing the components of the starting vectors and the final resulting vector after vector algebra. Vector algebra is also defined for n-dimensions in general, beyond just the 2 or 3 dimensions. Many different types of data are better organized as vectors, such as the prices of 6 different ingredients for a product or the 4-dimensional vectors in physics, to account for 3D space and the time component.

The timestamps of key parts of the video are listed below:

• Adding Vectors Algebraically: 0:00
• Subtracting Vectors Algebraically: 3:55
• Scalar Multiplication Algebraically: 7:36
• Vector Algebra Summary: 9:46
• Example 4: 10:24
• n-Dimensional Vectors: 16:49
• Note on n-Dimensional Vectors: 18:13

This video was taken from my earlier video listed below:

• Vectors and the Geometry of Space: Vectors: https://youtu.be/0lJiVlKw4Kc
• Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-vectors
• Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EiRECLVkBCcFhSpbSz8XIw

Related videos:

Vectors and Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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