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PROPERTIES of Surjective Linear Transformations | FREE Linear Algebra Course
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In this video, we show that surjective linear transformations preserve the spanning property. We also prove that composition of surjective linear transformations is a surjective linear transformation.
This video is part of a linear algebra course
Students often ask is linear algebra important and is linear algebra hard. They wonder can anyone learn linear algebra and why some can't understand linear algebra. It is important to show to the students how linear algebra is used in data science, machine learning, AI, computer science, image processing, computer graphics, and in real life in general. This is a free video course in linear algebra for everyone, even beginners. It covers linear algebra with applications.
CHAPTERS:
0:00 Intro and learning outcomes
0:41 Spanning set for range
3:20 Surjective linear transformations take bases to spanning sets
6:08 Surjective linear transformations and dimension
8:10 How to use dimension to show that a linear transformation is not surjective
9:05 Composition of surjective linear transformations is a surjective linear transformation
11:00 Now what?
#mathflipped
This video is part of a linear algebra course
Students often ask is linear algebra important and is linear algebra hard. They wonder can anyone learn linear algebra and why some can't understand linear algebra. It is important to show to the students how linear algebra is used in data science, machine learning, AI, computer science, image processing, computer graphics, and in real life in general. This is a free video course in linear algebra for everyone, even beginners. It covers linear algebra with applications.
CHAPTERS:
0:00 Intro and learning outcomes
0:41 Spanning set for range
3:20 Surjective linear transformations take bases to spanning sets
6:08 Surjective linear transformations and dimension
8:10 How to use dimension to show that a linear transformation is not surjective
9:05 Composition of surjective linear transformations is a surjective linear transformation
11:00 Now what?
#mathflipped
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