Determine if this is a vector space with the indicated operations(adsbygoogle = window.adsbygoogle || []).push({});

the set of V of all polynominals of degree >=3, togehter iwth 0, operations of P (P the set of polynomials)

now all the scalar multiplication axioms hold.

the text however says that the axion

[tex] \mbox{For u,v} \in V, \mbox{then} \ u+v \in V [/tex] does not hold

well ok take two polynomials

[tex] u(x) = a_{3} x^3 + ... + a_{n} x^n [/tex]

[tex] v(x) = b_{3} x^3 + ... + b_{k} x^k [/tex]

where both n,k>= 3, then suppose k< n

[tex] u(x) + v(x) = (a_{3} + b_{3}) x^3 + ... + (a_{k} + b_{k}) x^k + ... + a_{n} x^n [/tex]

which is certainly a polynomial or degree >= 3 isnt it?

It also applies for n<k and n = k

is the text book wrong?

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