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Answer:
a) 2B +5C
Explanation:
It is probably easiest to simply try the answer choices. You find the first one works, which means it is the one you want.
2B +5C = 2(4i -j) +5(2i +3j) . . . . choice (a)
= 8i -2j +10i +15j
= 18i +13j = A
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In general, you can solve for the coefficients p and q that make ...
pB +qC = A
p(4i -j) +q(2i +3j) = 18i +13j
(4p+2q)i +(-p +3q)j = 18i +13j
Equating the coefficients of i and j gives us 2 equations in p and q.
4p +2q = 18
-p +3q = 13
Adding 2 times the second equation to 1/2 the first, we get ...
1/2(4p +2q) +2(-p +3q) = 1/2(18) +2(13)
7q = 35
q = 5
Using the second equation to find p, we get ...
p = 3q -13 = 3(5) -13 = 2
These coefficients tell us ...
A = 2B +5C . . . . . . . matches choice (a)