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# Find a and b such that v = au + bw, where u = (1, 2) and w = (1, −1). v= (7,8) I got a=2 & b=1. Both answers are wrong Can anyone help me?

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- llafferLv 71 month agoFavorite Answer
I'm not sure if this is the way to do it, but if this works separately for the x's and the y's then we can break this up into two equations:

v = au + bw

u = (1, 2), w = (1, -1), and v = (7, 8)

If we set one up using the x's on the left equation and y's on the right equation we get:

7 = a(1) + b(1) and 8 = a(2) + b(-1)

7 = a + b and 8 = 2a - b

We now have a system of two equations and two unknowns. Solving the first equation for "a" in terms of "b":

7 = a + b

7 - b = a

Now to substitute that into the second equation and solve for b:

8 = 2a - b

8 = 2(7 - b) - b

8 = 14 - 2b - b

8 = 14 - 3b

-6 = -3b

2 = b

Now we can solve for a:

a = 7 - b

a = 7 - 2

a = 5

I get:

a = 5 and b = 2

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