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Defining subspaces of Rn and the three required properties
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Defining subspaces of Rn and the three required properties
32:12
About this lesson
Properties of Subspace Overview:
A Subspace in \( \Bbb{R}^n \)
• The zero vector
• Closed under addition
• Closed under scalar multiplication
• Example of a Subspace
• Example of not a Subspace
• The zero vector
• Closed under addition
• Closed under scalar multiplication
• Example of a Subspace
• Example of not a Subspace
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Video 1 of 7
Defining subspaces of Rn and the three required properties
32 min
• Selected
Proving a span of two vectors is a subspace using three properties
15 min
Testing if the upper half-plane in R2 is a subspace
13 min
Proving the set where x2 equals x1 is a subspace of R2
12 min
Showing a graphed region in R2 is not a subspace via scalar multiplication
8 min
Showing a shaded region fails closure under addition
10 min
Proving a span of three vectors is a subspace of R3
11 min