# Nonhomogeneous system of linear equations

1. May 19, 2012

### salistoun

Hi all,

How do u go about doing this question?

x - 2y +z =4
y- z =3
(a^2 - a - 2)z = a+1

Determine values of a for which the system has no solution, one solution and many solutions

Stephen

2. May 19, 2012

### chiro

Hey Stephen and welcome to the forums.

You should for this problem set up an augmented system and apply row-operations.

You could use MATLAB though and invert the matrix in terms an unknown number a and then check that you don't get an inconsistent system since a is in the RHS vector.

Show us what augmented system have and row operations to get your reduced system

3. May 19, 2012

### AlephZero

What Chiro said is true, but it's probably quicker to start by factorizing $(a^2 - a - 2)z = a+1$ into $(a+1)(a-2)z = a+1$, and thinking about when that equation has zero, one, or many solutions.