Question Solved1 Answer 9. Show that the vector \( \vec{a}=(5,9,14) \) can be written as a linear combination of the vectors \( \vec{b} \) and \( \vec{c} \), where \( \vec{b}=(-2,3,1) \) and \( \vec{c}=(3,1,4) \). (4 marks)

YPBWYO The Asker · Advanced Mathematics

Transcribed Image Text: 9. Show that the vector \( \vec{a}=(5,9,14) \) can be written as a linear combination of the vectors \( \vec{b} \) and \( \vec{c} \), where \( \vec{b}=(-2,3,1) \) and \( \vec{c}=(3,1,4) \). (4 marks)
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Transcribed Image Text: 9. Show that the vector \( \vec{a}=(5,9,14) \) can be written as a linear combination of the vectors \( \vec{b} \) and \( \vec{c} \), where \( \vec{b}=(-2,3,1) \) and \( \vec{c}=(3,1,4) \). (4 marks)
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Step1/1Let me discuss the problem with proper explanation---->(9)" Say, "{:[ vec(a)=(5","9","14)],[ vec(b)=(-2","3","1)],[ vec(c)=(3","1","4)]:}{:[" Say, " vec(a)=lambda_(1) vec(b)+lambda_(2) vec(c).],[=>(5","9","14)=lambda_(1)(-2","3","1)+lambda_(2)(3","1","4)],[=>quad-2lambda_(1)+3lambda_(2)=5rarr(1)],[3lambda_(1)+lambda_(2)=9rarr(11)],[lambda_(1)+4lambda_(2)=14 rarr(111)],[" (1) "xx3+(11)xx2=>] ... See the full answer