Let a_1=[[1],[3],[-1]],a_2=[[-6],[-14],[3]],b=[[5],[3],[h]]. for what value(s) of h is b in

William Boggs

William Boggs

Answered question

2021-12-13

Let a1=[131],a2=[6143],b=[53h]. for what value(s) of h is b in the plane spanned by a1 and a2

Answer & Explanation

Ana Robertson

Ana Robertson

Beginner2021-12-14Added 26 answers

b in the plane spanned by a1 and a2 if b is the linear combination of a1 and a2.
b=θ1a1+θ2a2
[53h]=α1[131],α2=[6143]
5=α16α21
3=3α114α22
h=α13α23
1×315=3α118α2
23=3α114α2
Subtract, 12=14α2α2=3
Sub α2=3 in 1, 5=α1+18
α1=13
Sub α1=13 and α2=3 in 3,
h=13+3(3)=139=4
i.e h=4
Paul Mitchell

Paul Mitchell

Beginner2021-12-15Added 40 answers

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