Find polynomial p_1 and p_2 in P^2 that spans the kernel of T and describes the range of sf "T".

fortdefruitI 2020-11-20 Answered

Find polynomial p1andp2P2 that spans the kernel of T and describes the range of sf "T".

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Expert Answer

Sadie Eaton
Answered 2020-11-21 Author has 104 answers

The linear transformation T is defined as sf T:P2R2by(p)=[p(0)p(0)]
The set of polynomial p in P2 such that T(p)0, are the members of kernel of T.
Therefore, any quadratic polynomial p with properties p(0)=0 will be in kernel of T.
Thus, the two polynomials p1(t)=tandp2(t)= wil be in kernel of T.
The polynomial t and t2 linearly independent.
Thus, the linear combination of t and t2 will be in kernel of T.
Hence, the polynomials p1(t)=tandp2(t)=t2 spans the kernel of T.
The set of all polynomial contained in range of T is {pV:T((p)}
The value of p (0) is always constant.
Thus, the range of T is given by {[cc]:cisR}.
The range of T is {[cc]:cisR}.

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