Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

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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  • 1 month ago
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    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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