x2+x2+2x3=8-x1-2x2+3x3=13x1-7x2+4x3=10

Sinthiya Shaheen

Sinthiya Shaheen

Answered question

2022-06-12

x2+x2+2x3=8

-x1-2x2+3x3=1

3x1-7x2+4x3=10

Answer & Explanation

madeleinejames20

madeleinejames20

Skilled2023-05-20Added 165 answers

Write the system of equations in augmented matrix form:
[0112|8123|1374|10]
Perform row operations to eliminate the coefficients below the main diagonal. Our goal is to transform the matrix into row-echelon form (also known as reduced row-echelon form).
Multiply the first row by 3 and add it to the third row:
[0112|8123|1047|34]
Next, multiply the second row by -1 and add it to the first row:
[132|7123|1047|34]
Multiply the second row by 3 and add it to the first row:
[132|7073|20047|34]
Multiply the second row by 17:
[132|70137|207047|34]
Multiply the second row by 4 and add it to the third row:
[132|70137|20700197|347]
Multiply the third row by 719:
[132|70137|207001|2]
Multiply the third row by 2 and add it to the first row:
[130|110137|207001|2]
Multiply the third row by 37 and add it to the second row:
[130|11010|27001|2]
Multiply the second row by 3 and add it to the first row:
[100|377010|27001|2]
The augmented matrix is now in row-echelon form. Extracting the coefficients, we obtain the solution:
x1=377
x2=27
x3=2
Therefore, the solution to the system of equations is:
x1=377
x2=27
x3=2

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