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Priyanka12081

  • 3 years ago

Prove that set of all fourth degree polynomials is not a vector space

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  1. Mikael
    • 3 years ago
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    Weelll, it is not so simple to prove a false assertion....

  2. Mikael
    • 3 years ago
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    Since it is closed to linear combinations and closed to multiplication by a scalar - it IS a vector space. 4-Dimensional by the way.

  3. Mikael
    • 3 years ago
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    Sorry - 5 dimensional

  4. Priyanka12081
    • 3 years ago
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    cud u plz tell me the exact steps to write :) :)

  5. Mikael
    • 3 years ago
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    I know what your Lecturer/book THINKS ( and he/she is wrong !) - it thinks that P(x) = 7x +3 is not 4-th degree. But unfortunately for him/her it formally IS

  6. Mikael
    • 3 years ago
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    Consider the set of all expressions of the form\[\sum_{i=0}^{4} a_i * x^i\] where a_i are real/complex and x is a formal letter.

  7. Mikael
    • 3 years ago
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    Adding the Linear combination of two objects like that will always result in the same FORM\[\sum_{i=1}^{4} a_i x^i + \sum_{i=1}^{4} b_i x^i = \sum_{i=1}^{4} (a_i + b_i) x^i\]

  8. Mikael
    • 3 years ago
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    The fact that sometimes a_4 + b_4 = 0 shall not be of any problem

  9. Priyanka12081
    • 3 years ago
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    Thanks :)

  10. Mikael
    • 3 years ago
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    Thanks @Priyanka12081

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