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Also on matrices

  1. Jun 3, 2006 #1
    find the values of 'a' for which the equations { ax + y = 7}
    { 4x + ay = 19}
    have no solutions.

    I realise that you have to split it into

    (a 1) (x) (7)
    (4 a) (y) = (19)

    but I am stuck how to find solutions for 'a'

    any help would be great thanks
     
  2. jcsd
  3. Jun 3, 2006 #2

    arildno

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    Note that this can only happen if the deteminant of your matrix is 0..
     
  4. Jun 3, 2006 #3

    dav2008

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    As arildno said, if the determinant of the matrix[tex] A = \left(
    \begin{array}{cc}
    a & 1\\
    4 & a
    \end{array}
    \right)[/tex] is 0 then the equation has no solutions. (Or infinitely many)

    Why is this? To solve for x and y you have to multiply both sides by [tex]A^{-1}[/tex]. For [tex]A[/tex] to be invertible, what must be true of the determinant of [tex]A[/tex]?
     
    Last edited: Jun 3, 2006
  5. Jun 4, 2006 #4
    but the answer in the book says +/- 2 how is that
     
  6. Jun 4, 2006 #5
    'a' can have multiple values; that is, there are multiple matrices for which those equations have no solutions.

    Note if you take the determinant of that matix and solve for 'a' you get a quadratic with two solutions.
     
  7. Jun 4, 2006 #6

    HallsofIvy

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    So far you haven't given any indication that you have understood or tried using the hints given. What is the determinant of that matrix?
    What equation for a do you get if you set the determinant equal to 0? What are the solutions to that equation?
     
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