Give a full correct answer for given question

CoormaBak9 2020-11-01 Answered

Give a full correct answer for given question 1- Let W be the set of all polynomials a+bt+ct2P2 such that a+b+c=0 Show that W is a subspace of P2, find a basis for W, and then find dim(W) 2 - Find two different bases of R2 so that the coordinates of b=[53] are both (2,1) in the coordinate system defined by these two bases

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joshyoung05M
Answered 2020-11-02 Author has 97 answers

Consider W={a+bt+ct2;a+b+c=0} Yes.W is a subspace of P2. Since 0ϵW. If x+yt+zt2andl+mt+nt2 are elements of P2, then (x+l)+(y+m)t+(z+n)t2ϵW. So w is closed under vector addtion. Let rϵR and a+bt+ct2ϵW then r(a+bt+ct2)=ra+rbt+rct2ϵW. Therefore w is closed under scalar multiplication . Therefore W is a subspace of P2.

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