Recent content by MDolphins

  1. M

    Prove that ℝ has no subspaces except ℝ and {0}.

    So going back to the proof, the real numbers and 0 are the only subspaces of R bc they seethe only sets that hold under. Scalar multiplication.
  2. M

    Prove that ℝ has no subspaces except ℝ and {0}.

    It is not a sunspace because it is not closed under multiplication.
  3. M

    Prove that ℝ has no subspaces except ℝ and {0}.

    No 3 is not. The sunspace (-2,2) does not contain all of the real numbers of R. For example 3.
  4. M

    4x4 matrix A where A^2 and A^3 do not equal A, but A^4 = A

    Okay so now I have the angles, how can I visualize where I want the numbers in the4 x 4 matrix
  5. M

    Prove that ℝ has no subspaces except ℝ and {0}.

    True
  6. M

    Prove that ℝ has no subspaces except ℝ and {0}.

    Is (-2,2) not a sunspace because all the scalers are of the natural numbers?
  7. M

    4x4 matrix A where A^2 and A^3 do not equal A, but A^4 = A

    Oh okay so would it be by 120 degree angles. A2 would be 120 a3 would be 240 A4 would be 360 or the initial A
  8. M

    4x4 matrix A where A^2 and A^3 do not equal A, but A^4 = A

    You are right. You'd want 270 degrees right?
  9. M

    4x4 matrix A where A^2 and A^3 do not equal A, but A^4 = A

    I could come up with a rotation matrix that was 180 degrees but not one that was 360 degrees
  10. M

    Prove that ℝ has no subspaces except ℝ and {0}.

    I'm confused as to why (-2,2) is not a subspace. I am lost.
  11. M

    Prove that ℝ has no subspaces except ℝ and {0}.

    Well, the closure property holds for v, because since v is a part of the reals, any real number times v will still be apart of the reals. Therefore, the only subspace of the reals are the reals and {0}?
  12. M

    Prove that ℝ has no subspaces except ℝ and {0}.

    So to show that w is in the vector space V, would I assume that it is not. Then, go on to show that if it is not it is not a part of the real numbers. However, under the assumption I said w is apart of the real numebrs, therefore a contradiciton.
  13. M

    4x4 matrix A where A^2 and A^3 do not equal A, but A^4 = A

    The question is, find a 4x4 matrix A where A^2 and A^3 do not equal A, but A^4 = A. So far, I have tried matrixes all involving 1's and 0's and -1's. I have also tried to use examples of nilpotent matrixes. However, I have not found anything close.
  14. M

    Prove that ℝ has no subspaces except ℝ and {0}.

    Well, if we were to look at a subspace that is not in ℝ, it would not be closed under the same addition or multiplication that is in ℝ. And additionally, from the theorem "if a subset S of a vector space V does not contain the zero vector 0 of V, then S is not a subspace of V". From this, the 0...
  15. M

    Prove that ℝ has no subspaces except ℝ and {0}.

    would i use contradiction