Examples of SubSpaces and Non SubSpaces of Polynomial Space

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In this video we will see subsets of polynomial space which are subspace and which are not subspace.

Set of all polynomials whose degree is almost n ( less equal n) forms a subspace of polynomial subspace.
Set of all polynomials whose degree is = n ( equal to n) do not form a subspace of polynomial subspace.
Set of all polynomials whose degree is greater than n do not form a subspace of polynomial subspace.
Set of all polynomials such that p(0)=0 forms a subspace.
Set of all polynomials such that p(0)=1 do not form a subspace.

[SiniDhurua]

Sir in polynomial of degree 3 there is missing of zero vector but sir we can express 0 as 3 degree polynomial so why there is missing plz help me sir

[Shiksha]

Sir if degree of n greater than equal 1 h to tb ye subspace hoga ya nhi... please reply

[thetechblogger]

Sir I didn't get one question. The question is ' Let V=P2(R). Then W={a0x^2+a1x+a2 belongs to P2 : a0+a1=0} is the subspace of V or not?

[mathematicalsociety]

sir agr hm x ki power n positive lyn to wo W ko belong krta hy phr wo subspace ho gi

[Learnwithme.]

Is polynomial at most degree 2 a subspace if p’(x) = x?

[navjotzsingh]

Sir why 3 degree polynomial is not a vector space ..
If it is ..then how?
Plz help me with this doubt

[lightdevil]

What If U = { f € P/f has rational coefficient} is subspace or not???

[thetechblogger]

Let V=P2(R). Then which of the following subsets of V are subspace of V.
i. S1={p belongs to V: p'(1)=0}
ii. S2= {p belongs to V: p(-1)=1}
Sir I am confused on how to start this ques.

[joicet]

sir can you prove a polynomial with degree >=n

[thetechblogger]

Sir please suggest a way to prepare theorems?
Sir can you prepare a lec on Span of Subset?

[ojosworld]

Sir can you solve this set as a subspace of P
i.e
{p€P / degree of p=4 }
This set is not subspace can you give us example for this plz.

[ankitchowdhury]

How to find dimension of a subspace such that p(x)=p(2x) is satisfied