Hais txog kev ncua, ib txheej ntawm vectors yog linearly ywj siab yog tias nws tsis muaj vectors tsis tsim nyog, uas tsis yog vector yog nyob rau ntawm lwm tus. Yog li peb muab tag nrho cov no ua ke hauv qhov tseem ceeb hauv qab no theorem. nws ua raws li txhua tus coefficient ai=0. Tsis muaj vector nyob rau ntawm qhov ntev ntawm lwm tus.
Yuav ua li cas koj thiaj paub yog hais tias ib tug span yog linearly ywj siab?
Cov txheej vectors yog linearly ywj siab yog tsuas yog linear ua ke ua 0 yog qhov tsis tseem ceeb nrog c1=···=cn=0. Xav txog ib txheej uas muaj ib tug vector v. piv txwv, 1v=0. ▶ Yog v=0 ces tsuas scalar c xws li cv=0 yog c=0.
Cov txheej twg yog linearly ywj siab?
Nyob rau hauv txoj kev xav ntawm vectors qhov chaw, ib txheej vectors tau hais tias yog linearly dependent yog tias muaj cov kab sib txuas tsis sib xws ntawm vectors uas sib npaug ntawm xoom vector. Yog tias tsis muaj qhov sib xyaw ua ke no tshwm sim, ces cov vectors tau hais tias yog linearly ywj siab.
Koj paub li cas yog tias txoj haujlwm yog linearly ywj siab?
Yog Wronskian W(f, g)(t0) is nonzero for some t0 in [a, b] then f thiab g yog linearly ywj siab ntawm [a, b]. Yog tias f thiab g yog linearly dependent ces Wronskian yog xoom rau tag nrho t hauv [a, b]. Qhia tias functions f(t)=t and g(t)=e2t yog linearly ywj siab. Peb suav cov Wronskian.
Puas yog sin 2x thiab cos 2x linearly ywj siab?
Vim li no, qhov no qhia tias sin2(x) thiab cos2(x) yog linearly ywj siab.
