The final matrix is in the desired form: 9,-1,-1.
Let's solve the given system of equations using Gauss-Jordan elimination:
The system of equations is:
10x+y =4
x+ y+ z =7
x−2z =11
We can represent this system as an augmented matrix:
⎡ 10 1 0 | 4 ⎤
1 1 1 | 7
⎣ 1 0 -2 | 11 ⎦
Now, let's perform row operations to transform this matrix into reduced row-echelon form:
1. R2= R2- 1/10 R1
2. R3 = R3 - 1/10 R1
3. R3 = R3 -R2
4. R1 =R1- R2
5. R1 = R1+ 2R3
6. R2 = R2 -R3
After these operations, the matrix becomes:
⎡ 1 0 0 | 9 ⎤
0 1 0 | -1
⎣ 0 0 1 | -1 ⎦
So, the solution to the system of equations is x=9,y=−1,z=−1.
The matrix is in the required form [010].
This indicates that the system has a unique solution, and the values for x, y, and z are 9, -1, and -1, respectively.