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Priyanka12081
 3 years ago
Prove that set of all fourth degree polynomials is not a vector space
Priyanka12081
 3 years ago
Prove that set of all fourth degree polynomials is not a vector space

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Mikael
 3 years ago
Best ResponseYou've already chosen the best response.3Weelll, it is not so simple to prove a false assertion....

Mikael
 3 years ago
Best ResponseYou've already chosen the best response.3Since it is closed to linear combinations and closed to multiplication by a scalar  it IS a vector space. 4Dimensional by the way.

Priyanka12081
 3 years ago
Best ResponseYou've already chosen the best response.0cud u plz tell me the exact steps to write :) :)

Mikael
 3 years ago
Best ResponseYou've already chosen the best response.3I know what your Lecturer/book THINKS ( and he/she is wrong !)  it thinks that P(x) = 7x +3 is not 4th degree. But unfortunately for him/her it formally IS

Mikael
 3 years ago
Best ResponseYou've already chosen the best response.3Consider 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.

Mikael
 3 years ago
Best ResponseYou've already chosen the best response.3Adding the Linear combination of two objects like that will always result in the same FORM\[\sum_{i=1}^{4} a_i x^i + \sum_{i=1}^{4} b_i x^i = \sum_{i=1}^{4} (a_i + b_i) x^i\]

Mikael
 3 years ago
Best ResponseYou've already chosen the best response.3The fact that sometimes a_4 + b_4 = 0 shall not be of any problem
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