Let a =(1, 1,1), b =(−1, 3, 2,), c =(−3, 0,1),d =(4,−1,1) (b)Find scalars A,B,C such that d =Aa +Bb +Cc.

acsuvaic9

acsuvaic9

Answered question

2022-07-25

Let a =(1, 1,1), b =(−1, 3, 2,), c =(−3, 0,1),d =(4,−1,1)
(b)Find scalars A,B,C such that d =Aa +Bb +Cc.

Answer & Explanation

Jaylene Tyler

Jaylene Tyler

Beginner2022-07-26Added 10 answers

If d=Aa+Bb+Cc,then this relation works component-wise as well.
Equating components, we have the following system of linear equations:
A-B-3C=4
A+3B=-1
A+2B+C=1.
A=-1-3B.
-1-4B-3C=4
-1-B+C=1
-4B-3C=5
-B+C=2
C=2+B
-4B-6-3B=5
-7B=11
B=-11/7
C=3/7
A=26/7.
Darian Hubbard

Darian Hubbard

Beginner2022-07-27Added 7 answers

set up a system of 3 eq and 3 unkowns
A-B-3C=4
A+3B=-1
A+2B+c=1
solve this using various methods
B=-4/7
A=5/7
C=-19/21

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