Question

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

Answer 1

Weelll, it is not so simple to prove a false assertion....

Answer 2

Since it is closed to linear combinations and closed to multiplication by a scalar - it IS a vector space. 4-Dimensional by the way.

Answer 3

Sorry - 5 dimensional

Answer 4

cud u plz tell me the exact steps to write :) :)

Answer 5

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

Answer 6

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.

Answer 7

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

Answer 8

The fact that sometimes a_4 + b_4 = 0 shall not be of any problem

Answer 9

Thanks :)

Answer 10

Thanks @Priyanka12081