Question

Solve the following system of equations using the Gauss elimination method:

A) x = -1, y = 2, z = 3
B) x = 1, y = 1, z = -1
C) x = 2, y = -1, z = -2
D) x = -2, y = 0, z = 1

Answer 1

To solve the system of equations using the Gauss elimination method, perform row operations to convert the matrix into row-echelon form. Once in row-echelon form, solve for the values of x, y, and z.

Step-by-step explanation:

To solve the system of equations using the Gauss elimination method, we'll start by writing the equations in matrix form. Let's call the first equation as Equation 1, the second equation as Equation 2, and the third equation as Equation 3. The matrix form of the system is:

[1 0 0 -1]
[0 1 0 2]
[0 0 1 3]

Using the Gauss elimination method, we'll perform row operations to get the matrix in row-echelon form. Once we reach row-echelon form, we can easily solve for the values of x, y, and z.

Let's perform the row operations:

1. Multiply Equation 1 by -1
2. Add Equation 1 to Equation 2
3. Subtract 2 * Equation 1 from Equation 3
4. Divide Equation 2 by 3
5. Add (-2 * Equation 2) to Equation 3
6. Divide Equation 3 by 3

After performing these row operations, we'll have the matrix in row-echelon form:

[1 0 0 -1]
[0 1 0 -2]
[0 0 1 3]

Now we can easily solve for the values of x, y, and z. From the row-echelon form, we can see that x = -1, y = 2, and z = 3.