System of Equations: Unique Solution Conditions

[emilieloops]

Homework Statement

Under what condition will the following system have a unique solution?

x -y +2z = 1
ax -ay +4z = 2a
x +y +az = 4

Note: a is a parameter.

The Attempt at a Solution

I know I'm supposed to solve by turning this into the identity matrix by I really have no idea where to start. Hellp would be much appreciated.

 

[UltrafastPED]

Rewrite the equation in matrix form:

1 -1 2 x 1
a -a 4 * y = 2a
1 1 a z 4

This system is has a unique solution if the matrix on the LHS has an inverse.

From your (3) it seems that you are to use Gaussian elimination:
http://en.wikipedia.org/wiki/Gaussian_elimination

Depending on how you set this up it can provide the inverse matrix and the solution.

 

[emilieloops]

Rewrite the equation in matrix form:

1 -1 2 x 1
a -a 4 * y = 2a
1 1 a z 4

This system is has a unique solution if the matrix on the LHS has an inverse.

From your (3) it seems that you are to use Gaussian elimination:
http://en.wikipedia.org/wiki/Gaussian_elimination

Depending on how you set this up it can provide the inverse matrix and the solution.

Can I ignore the right side of all the equations in order to find the inverse?

 

[Mark44]

Yes.