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anonymous

  • 5 years ago

Help with proving W = (1,2,4x+3Y) not a vector

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  1. anonymous
    • 5 years ago
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    are there any more details to this question?

  2. anonymous
    • 5 years ago
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    x and y are real numbers and V = R3

  3. anonymous
    • 5 years ago
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    Help with proving W = (1x,2y,4x+3Y) not a vector , x and y are real numbers and V = R3

  4. anonymous
    • 5 years ago
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    not a vector or not a vector space?

  5. anonymous
    • 5 years ago
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    not a vector sub space

  6. anonymous
    • 5 years ago
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    okay, makes more sense now

  7. anonymous
    • 5 years ago
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    it appears to pass the conditions to be a subspace of R^3

  8. anonymous
    • 5 years ago
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    how to prove with addition

  9. anonymous
    • 5 years ago
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    Let \[\vec{a}=(x_1,2y_2,4x_1+3y_1)\] and \[\vec{b}=(x_2,y_2,4x_2+3y_2)\] be in W

  10. anonymous
    • 5 years ago
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    Now \[\vec{a}+\vec{b}=(x_1+x_2,y_1+y_2,4x_1+3y_1+4x_2+3y_2)\] group and factor the third component to get \[(x_1+x_2,y_1+y_2,4(x_1+x_2)+3(y_1+y_2))\]

  11. anonymous
    • 5 years ago
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    since \[x_1,x_2,y_1,y_2\in \mathbb{R}\] clearly this vector sum of arbitrary vectors in W is in W

  12. anonymous
    • 5 years ago
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    I should have made the statement about \[x_1,x_2,y_1,y_2\in \mathbb{R}\] first of course

  13. anonymous
    • 5 years ago
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    Thank you I am reviewing to make sure I understand.

  14. anonymous
    • 5 years ago
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    would it work the same if W = x,2y,4x - 3Y

  15. anonymous
    • 5 years ago
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    it should, but I have not tried it, Proving a subspace is one of those "turn the crank" type proofs in linear algebra that may seem a little abstract at first but once yo get the process down is straight forward but sometimes tedious...

  16. anonymous
    • 5 years ago
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    Thank You

  17. anonymous
    • 5 years ago
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    IS W subspace of V, W is the set of all functions F(0)=1 , V=C(\[-\infty\],\[\infty\])

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