Properties of subspace

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Intros
Lessons
  1. Properties of Subspace Overview:
  2. A Subspace in Rn \Bbb{R}^n
    • The zero vector
    • Closed under addition
    • Closed under scalar multiplication
    • Example of a Subspace
    • Example of not a Subspace
  3. Subspace of a span of vectors in Rn \Bbb{R}^n
    • Remember span = linear combination
    • Showing a span of vectors is a subspace in Rn\Bbb{R}^n
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Examples
Lessons
  1. Showing that a set is a subspace of Rn\Bbb{R}^n
    Is the following set a subspace of R2\Bbb{R}^2?
    Is this set a subspace of R^2
    1. Is the following set a subspace of R2\Bbb{R}^2?
      Is this set a subspace of R^2
      1. Showing that a set is a subspace of Rn\Bbb{R}^n with graphs
        The following graph displays a set in R2\Bbb{R}^2. Assume the set includes the bounding lines. Give a reason as to why the set SS is not a subspace of R2\Bbb{R}^2.
        graph of a set in R^2, graph 1
        1. Showing that a set is a subspace of Rn\Bbb{R}^n with graphs
          The following graph displays a set in R2\Bbb{R}^2. Assume the set includes the bounding lines. Give a reason as to why the set SS is not a subspace of R2\Bbb{R}^2.
          graph of a set in R^2, graph 2
          1. Showing a set equal to a span of vectors is a subspace of Rn\Bbb{R}^n
            Let U=U= Span{v1,v2,v3v_1,v_2,v_3}, where UU is a set. Determine if UU is in the subspace of R3\Bbb{R}^3.