Answer :
3x1+9x2+6x318x1+48x2+39x39x1−27x2+42x3=4.6=27.2=9.0 the system of equations has no solution.
The equation you provided is:
3x1 + 9x2 + 6x3 = 18
x1 + 3x2 + 2x3 = 6
9x1 - 27x2 + 42x3 = 4.6
To solve this system of linear equations, we can use the method of Gaussian elimination or matrix operations. Let's solve it using Gaussian elimination:
Step 1: Write the augmented matrix of the system:
Copy code
3 9 6 | 18
1 3 2 | 6
9 -27 42 | 4.6
Step 2: Perform row operations to get the matrix in row-echelon form.
Row 2 = Row 2 - (1/3) * Row 1
Row 3 = Row 3 - 3 * Row 1
The matrix becomes:
Copy code
3 9 6 | 18
0 0 -2 | -2
0 -54 24 | -49.4
Step 3: Perform additional row operations to achieve reduced row-echelon form.
Row 3 = Row 3 - (-54/2) * Row 2
The matrix becomes:
Copy code
3 9 6 | 18
0 0 -2 | -2
0 0 -1 | -11.4
Step 4: Multiply Row 3 by -1/2 to simplify the matrix.
Row 3 = (-1/2) * Row 3
The matrix becomes:
Copy code
3 9 6 | 18
0 0 -2 | -2
0 0 1 | 5.7
Step 5: Perform row operations to eliminate the entries above and below the leading entry in the third column.
Row 1 = Row 1 - 6 * Row 3
Row 2 = Row 2 + 2 * Row 3
The matrix becomes:
Copy code
3 9 0 | -7.2
0 0 0 | -8.6
0 0 1 | 5.7
Step 6: The system is inconsistent since the second row of the matrix leads to an equation 0 = -8.6, which is not possible.
Therefore, the system of equations has no solution.
To know more about equations, visit:
https://brainly.com/question/17145398
#SPJ11
