# How can I justify whether I'm able to apply the Gaussian elimination method to this system?

I'm currently practicing some Gaussian elimination questions for my discrete math topic, I came across this question and I need help. How can I justify whether I'm able to apply the Gaussian elimination method to this system?

Question:

Consider the following system of linear equations.

$$\begin{eqnarray*}a_{12}y + a_{13}z &=& b_1 \\ a_{21}x + a_{23}z &=& b_2 \\ a_{31}x + a_{32}y &=& b_3\end{eqnarray*}$$

Can you apply Gaussian elimination to this system? Justify your answer.

## 1 answer

I may be misunderstanding the question, but technically you can always use the Gaussian elimination method.

But perhaps what you meant to ask is: Will the method give you a unique solution? Sometimes you get no solutions, sometimes you get infinitely many solutions, and sometimes you get precisely one solution.

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