Answer:
To see the steps to the diagonal form see the step-by-step explanation. The solution to the system is ,
,
and
Step-by-step explanation:
Gauss elimination method consists in reducing the matrix to a upper triangular one by using three different types of row operations (this is why the method is also called row reduction method). The three elementary row operations are:
To solve the system using the Gauss elimination method we need to write the augmented matrix of the system. For the given system, this matrix is:
For this matrix we need to perform the following row operations:
After this step, the system has an upper triangular form
The triangular matrix looks like:
If you later perform the following operations you can find the solution to the system.
After this operations, the matrix should look like:
Thus, the solution is:
,
,
and
