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  • Why R2 is not a subspace of R3? - Physics Forums
    R^2 is isomorphic to the subset (a,b,0) of R^3, but it's also isomorphic to infinitely many other subspaces of R^3 (any 2 dimensional one) As such, there's no canonical embedding, and you don't usually think of R^2 as being contained in R^3 A more obvious explanation is the vector (a,b) is not the same as the vector (a,b,0) 2 components vs 3 components, so they are different objects
  • Solving Vector Subspace Questions: A B in V - Physics Forums
    Prove your answer b) Determine whether or not A ∪ B is a vector subspace of V Prove your answer My strategy for this is to find two subspaces in V and find a counter claim so that the union of A and B is not a subspace and similarly for the intersection of A and B would this be strategy be enough to answer the question? thanks so much
  • Subspaces in R4: Get Started Understand Now - Physics Forums
    I'm so lost! 1 W is the set of all vectors in R4 such that x1 + x3 = x2 + x4 Is W a subspace of R4 and Why? How do i get started here? I'm thoroughly confused on this whole idea of vector spaces and such
  • Dimension of a vector space and its subspaces - Physics Forums
    My thought was that was a vector space and a subspace with an uncountably infinite index I then confused index and dimension instead of building a correct counterexample
  • What is a Closed Linear Subspace? - Physics Forums
    Here's an example, "If L is a closed linear subspace of H, then the set of of all vectors in H that are orthogonal to every vector in L is itself a closed linear subspace" But 'closed linear subspace' definitely means something different to just 'linear subspace', because the authors only describe some linear subspaces as 'closed'
  • Prove the sum of two subspaces is also a subspace.
    Homework Equations is a subspace of if is also a vector space and it contains the additive identity, is closed under addition, and closed under scalar multiplication The definition of a sum a vector subspace U and W is The Attempt at a Solution 1 Since and both contain the additive identity, contains the additive identity 3
  • Distance from a vector to a subspace - Physics Forums
    Similar threads I Vector subspace and basis vectors in the context of data science Mar 17, 2024 Replies 6 Views 3K MHB -311 1 5 8 Ax=b in parametric vector form,
  • Is singular matrix is a subspace of vector space V? - Physics Forums
    a)is S closed under addition? b) is S closed under scalar multiplication? Homework Equations S is a subspace of V if it is closed under addition and scalar multiplication The Attempt at a Solution I tried to use the definition of sinularity i e a matrix in not invertible But could not decide if it was closed under addition and scalar




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