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Math Help - Linearly independent vectors

  1. #1
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    Linearly independent vectors

    "Suppose x and y are linerarly independent vectors satisfying the following vector equation:
    -4x + α(x+y) = β(x-3y).
    Find α and β.

    I tried solving the vector equation however, I can only find a correctly and as for β, it is the wrong sign. So, I am pretty sure I made at least some error in my working.
    Working:
    -> (-4 + α + β)x = (α - 3β)y
    -> -4 + α + β = 0 = 2 - 3B
    -> α + B = 4, α - 3β = 0
    -> β = 4 - α, α - 3(4 - α) = α - 12 + 3α = 4α - 12
    -> α = 3, B = 1

    (β is supposed to be -1 so, I know I made some error there but I'm unsure as to what I did incorrectly though.)
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  2. #2
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    Quote Originally Posted by cottontails View Post
    "Suppose x and y are linerarly independent vectors satisfying the following vector equation:
    -4x + α(x+y) = β(x-3y).
    Find α and β.

    I tried solving the vector equation however, I can only find a correctly and as for β, it is the wrong sign. So, I am pretty sure I made at least some error in my working.
    Working:
    -> (-4 + α + β)x = (α - 3β)y


    It must be -\beta in the LHS parentheses and -\alpha in the RHS's one.

    Tonio


    -> -4 + α + β = 0 = 2 - 3B
    -> α + B = 4, α - 3β = 0
    -> β = 4 - α, α - 3(4 - α) = α - 12 + 3α = 4α - 12
    -> α = 3, B = 1

    (β is supposed to be -1 so, I know I made some error there but I'm unsure as to what I did incorrectly though.)
    .
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