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

1. Mikael

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

2. Mikael

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

Sorry - 5 dimensional

4. Priyanka12081

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

5. Mikael

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

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

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

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

9. Priyanka12081

Thanks :)

10. Mikael

Thanks @Priyanka12081