No. Ob tug vectors tsis tau R3.
Vim li cas 2 vectors tsis span R3?
Cov vectors ncua R3. tsis tsim lub hauv paus rau R3 vim cov no yog kab vectors ntawm matrix uas muaj ob kab zoo tib yam. Peb vectors tsis yog linearly ywj siab. Feem ntau, n vectors hauv Rn tsim ib lub hauv paus yog tias lawv yog kab vectors ntawm invertible matrix.
Ua vectors span R3?
Vim qhov ncua sij hawm muaj cov qauv hauv paus rau R3, nws muaj tag nrho R3 (thiab yog li sib npaug rau R3). rau arbitrary a, b, thiab c. Yog tias ib txwm muaj kev daws teeb meem, ces cov vectors ncua R3; Yog tias muaj kev xaiv ntawm a, b, c uas lub kaw lus tsis sib haum, ces cov vectors tsis ncua R3.
R3 puas tuaj yeem cuam tshuam los ntawm 4 vectors?
Kev daws: Lawv yuav tsum muaj kev vam khom. Qhov loj me ntawm R3 yog 3, yog li txhua txheej ntawm 4 lossis ntau dua vectors yuav tsum yog nyob ntawm linearly. … Ib qho peb cov kab hluav taws xob ywj pheej hauv R3 yuav tsum ncua R3, yog li v1, v2, v3 kuj tseem yuav ncua R3.
Yuav tau 2 vectors hauv R3 ua linearly ywj siab?
Yog tias m > n ces muaj cov hloov pauv dawb, yog li cov tshuaj xoom tsis yog qhov tshwj xeeb. Ob vectors yog linearly dependent yog thiab tsuas yog lawv yog tib yam. … Yog li ntawd v1, v2, v3 yog linearly ywj siab. Plaub vectors nyob rau hauv R3 yog ib txwm linearly dependent.
