Answer :

3x1​+9x2​+6x3​18x1​+48x2​+39x3​9x1​−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:

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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:

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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:

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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:

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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:

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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.

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Rewritten by : Barada