Use gaussian elimination to write each system in triangular form
x+ y+z+ w= 1
x+y −w=−1
−x+ y+z+2w= 2
x+2y−z+ w= 0

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

cant see photo

step-by-step explanation: