Answer:
The solution of the system of linear equations is
Step-by-step explanation:
We have the system of linear equations:
Gauss-Jordan elimination method is the process of performing row operations to transform any matrix into reduced row-echelon form.
The first step is to transform the system of linear equations into the matrix form. A system of linear equations can be represented in matrix form (Ax=b) using a coefficient matrix (A), a variable matrix (x), and a constant matrix(b).
From the system of linear equations that we have, the coefficient matrix is
the variable matrix is
and the constant matrix is
We also need the augmented matrix, this matrix is the result of joining the columns of the coefficient matrix and the constant matrix divided by a vertical bar, so
To transform the augmented matrix to reduced row-echelon form we need to follow these row operations:
- multiply the 1st row by 1/2
- add -1 times the 1st row to the 2nd row
- add -3 times the 1st row to the 3rd row
- multiply the 2nd row by -2/7
- add 7/2 times the 2nd row to the 3rd row
- multiply the 3rd row by 1/3
- add 12/7 times the 3rd row to the 2nd row
- add 3 times the 3rd row to the 1st row
- add -3/2 times the 2nd row to the 1st row
From the reduced row echelon form we have that
Since every column in the coefficient part of the matrix has a leading entry that means our system has a unique solution.