Find values of a for which ax + y = 7 and 4x + ay = 19 have no solutions

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wayneo
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find the values of 'a' for which the equations { ax + y = 7}
{ 4x + ay = 19}
have no solutions.

I realize 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
 
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Note that this can only happen if the deteminant of your matrix is 0..
 
As arildno said, if the determinant of the matrix[tex]A = \left(<br /> \begin{array}{cc}<br /> a & 1\\<br /> 4 & a<br /> \end{array}<br /> \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]?
 
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but the answer in the book says +/- 2 how is that
 
'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.
 
wayneo said:
but the answer in the book says +/- 2 how is that
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?