Proving two Spans of Vectors are Equal Linear Algebra Proof  Summary and Q&A
TL;DR
This video provides a stepbystep proof that two spans in linear algebra are equal.
Questions & Answers
Q: What is the purpose of this video?
The purpose of this video is to demonstrate a direct proof of the equality of two spans in linear algebra without relying on theorems.
Q: How is the equality of the spans shown?
The method of double inclusion is used, where it is shown that each vector in one span can be written as a linear combination of the vectors in the other span, and vice versa.
Q: How is a vector represented as a linear combination?
A vector X can be written as a linear combination of vectors by multiplying each vector by a scalar and adding them together.
Q: What is the significance of proving the equality of spans?
Proving the equality of spans is important in understanding linear independence and the relationships between vectors in linear algebra.
Summary & Key Takeaways

The video aims to prove that two sets of linear combinations of vectors are equal.

Using the method of double inclusion, the proof shows that both sets are subsets of each other.

The first direction is straightforward, while the second direction involves carefully rewriting one vector as a linear combination of the others.