Vectors/Calc

Find values of a, b, and c which satisfies the following equation:

a(2,1,0) + b(-3,4,5) + c(2,0,3)= (-4,10,7)

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  1. You will have to solve 3 equations in 3 unknowns

    2a - 3b + 2c = -4
    a + 4b = 10
    5b + 3c = 7

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    posted by Reiny
  2. I got that far i just wasn't sure how to solve for 3 different unknowns unless I represent some unknown as the same as another unknown in the question?

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  3. double the 2nd and subtract from the first
    -11b + 2c = -24 (#4)

    #4x 3 : ---> -33b + 6c = -72
    #3x 2 : ---> 10b + 6c = 14

    subtract them
    -43b = -86
    b = 2

    in #4 : -22 + 2c = -24 ,
    c = -1

    in #2 : a + 8 = 10
    a = 2

    a=2, b=2, c=-1

    check:

    2(2,1,0) + 2(-3,4,5) - 1(2,0,3)
    = (-4,10,7)
    = RS

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    posted by Reiny
  4. great thanks :)

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