Nonhomogeneous system of linear equations

[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

 

[chiro]

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

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

 

[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.