Kev daws teeb meem. Lo lus teb yog no. Txij li qhov dim P3(R)=4, tsis muaj cov txheej txheem ntawm peb lub npe tuaj yeem tsim tag nrho P3(R).
Ua cov polynomials ncua P3?
Yes! Lub teeb spans qhov chaw yog thiab tsuas yog hais tias nws muaj peev xwm daws tau rau,,, thiab nyob rau hauv cov nqe lus ntawm ib tug lej, a, b, c, thiab d. Tau kawg, kev daws qhov kev sib npaug ntawm qhov kev sib npaug tuaj yeem ua tiav raws li lub matrix ntawm coefficients uas tau txais txoj cai rov qab rau koj txoj kev!
P3 polynomial yog dab tsi?
A polynomial hauv P3 muaj qhov form ax2 + bx + c rau qee qhov tsis tu ncua a, b, thiab c. Xws li ib tug polynomial belongs rau subspace S yog a02 + b0 + c=a12 + b1 + c, los yog c=a + b + c, or0=a + b, los yog b=−a. Yog li cov polynomials hauv subspace S muaj daim ntawv a(x2 −x)+c.
Yuav tau 3 vectors span P3?
(d) (1, 0, 2), (0, 1, 0), (−1, 3, 0), thiab (1, −4, 1). Yog lawm. Peb ntawm cov vectors no yog linearly ywj siab, yog li lawv span R3. … Cov vectors no yog linearly ywj siab thiab ncua P3.
P3 R yog dab tsi?
2. (20) S 1, t, t2 yog tus qauv hauv paus ntawm P3, qhov chaw vector ntawm polynomials ntawm degree 2 lossis tsawg dua.
