# Also on matrices

1. Jun 3, 2006

### wayneo

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. Jun 3, 2006

### arildno

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

3. Jun 3, 2006

### dav2008

As arildno said, if the determinant of the matrix$$A = \left( \begin{array}{cc} a & 1\\ 4 & a \end{array} \right)$$ 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 $$A$$?

Last edited: Jun 3, 2006
4. Jun 4, 2006

### wayneo

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

5. Jun 4, 2006

### 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.

6. Jun 4, 2006

### HallsofIvy

Staff Emeritus
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?