For which value of k the vector u=[[1],[-2],[k]] is a

interdicoxd 2022-01-04 Answered
For which value of k the vector u=[12k] is a linear combination of the vectors v1=[302] and v2=[215].
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Expert Answer

Elois Puryear
Answered 2022-01-05 Author has 30 answers
put the given values in the equation u=αv1+βv2
[12k]=α[302]β[215]
Now solve the given system get
3α+2β=1...(i)
0αβ=2...(ii)
2α5β=k...(iii)
Now find the value of α,β using equations i and ii
From equation (ii)
β=2
β=2
Put this value in equation i and solve for α
3α+2(2)=1
3α+4=1
3α=3
α=1
Now put the value of α,β in equation (iii) and solve it for k
2(1)5(2)=k
210=k
k=8
Answer:
Value of k is -8
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