Given a system
![](../../Assets/Images/Img548.png)
, a unique solution
![](../../Assets/Images/Img549.png)
exists
![](../../Assets/Images/Img551.png)
is invertible. This solution can be found using the following rule:
where
![](../../Assets/Images/Img553.png)
is the matrix
![](../../Assets/Images/Img554.png)
with the
![](../../Assets/Images/Img555.png)
th column replaced by the constant vector
![](../../Assets/Images/Img556.png)
.
Excercise 5-2. Solve the following system using Cramer's rule:
The system can be written in the following matrix form:
Thus, the required determinants are given by the following:
The solutions are given by the following: