Find 'a' Values for Ax + Y = 7 & 4X + Ay = 19

[wayneo]

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

 

[arildno]

Note that this can only happen if the deteminant of your matrix is 0..

 

[dav2008]

As arildno said, if the determinant of the matrixA = \left(<br /> \begin{array}{cc}<br /> a &amp; 1\\<br /> 4 &amp; a<br /> \end{array}<br /> \right) 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 A^{-1}. For A to be invertible, what must be true of the determinant of A?

 

[wayneo]

but the answer in the book says +/- 2 how is that

 

[jbusc]

'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.

 

[HallsofIvy]

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?