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Math Help - Vector transferring from the left side of the equation to the right

  1. #1
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    Exclamation Vector transferring from the left side of the equation to the right

    I have equation from the form a*b=c. where a is a row vector of [1*4] b is a column vector of [4*1] and c is a number. I want to get equation of the forum b=
    How can I do it?
    Thanks
    Ditza
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    Quote Originally Posted by ditzafar View Post
    I have equation from the form a*b=c. where a is a row vector of [1*4] b is a column vector of [4*1] and c is a number. I want to get equation of the forum b=
    How can I do it?
    Thanks
    Ditza
    I do not think you can get an equation for b.
    Becuase this is a dot product.
    But when you have a matrix product,
    A\bold{x}=\bold{b}
    Then,
    \bold{x}=A^{-1}\bold{b}
    Assuming "A" is an invertible matrix.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by ditzafar View Post
    I have equation from the form a*b=c. where a is a row vector of [1*4] b is a column vector of [4*1] and c is a number. I want to get equation of the forum b=
    How can I do it?
    Thanks
    Ditza
    Since u.v'=|u||v|cos(theta), where theta is the angle between u and v, there is no way of recovering v from the inner product.

    RonL
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  4. #4
    Super Member Rebesques's Avatar
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    Well... I think it can be done if we look at it as matrix multiplications. If the entries of a are nonzero, then the (4*1) vector d with entries the reciprocals of the entries of a, satisfies a*d=4, so if we multiply the equation a*b=c by d and treat everything as matrices (and since the associative law holds in this case), we get d*a*b=c*d or b=(c/4)*d. This is only a specific solution; The dot product - as Captainblack noted - guarantees there are infinitely many.

    Edit: In fact, four uknowns (the entries of b) minus one equation (ab=c --- this is only because of the dot product) we get three degrees of freedom for the solution. Will stop blabbering now.
    Last edited by Rebesques; February 11th 2007 at 06:01 AM.
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