Question The four vectors \[ \vec{a}_{1}=[1,2,2], \quad \vec{a}_{2}=[2,0,0], \quad \vec{a}_{3}=[3,-3,0], \quad \vec{a}_{4}=[1,1,1] \] span \( \mathbb{R}^{3} \) (in other words, their span equals \( \mathbb{R}^{3} \) ). Exactly one of the four vectors has the property that the span changes when you take it away. Which one? The four vectors a1=[1,2,2],a2=[2,0,0],a3=[3,−3,0],a4=[1,1,1] span R3 (in other words, their span equals R3 ). Exactly one of the four vectors has the property that the span changes when you take it away. Which one?
B9QXJM The Asker · Calculus
Transcribed Image Text: The four vectors a1=[1,2,2],a2=[2,0,0],a3=[3,−3,0],a4=[1,1,1] span R3 (in other words, their span equals R3 ). Exactly one of the four vectors has the property that the span changes when you take it away. Which one?
More Transcribed Image Text: The four vectors a1=[1,2,2],a2=[2,0,0],a3=[3,−3,0],a4=[1,1,1] span R3 (in other words, their span equals R3 ). Exactly one of the four vectors has the property that the span changes when you take it away. Which one?
Community Answer
YYXYR1
Given vectors{:[a_(1)=(1","2","2)quada_(2)=(2","0","0)a_(3)=(3","-3","0)],[a_(4)=(1","1","1)]:}Let us check whether (a_(1),a_(2),a_(3))(a_(2),a_(3),a_(4)).(a_(1)a_(2),a_(4))(a_(1)a_(3)a_(3)) span R^(3) or not-{:[[[a_(1),a_(2),a_(3)]]=[[1,2,2],[2,0,0],[-3,3,0]]],[[[1,2,2],[0,-4,-4],[0,9,.6]]larr{:[R_(2)-2R_(1)],[R_(3)+3R_(1).]:}],[{:[[1,2,2],[0,r,1],[0,3,2]]quadR_(3)rarrR_(3)-2R_(2):}],[[[1,2,2],[0,1 ... See the full answer