Question

Using the Cramer's rule to compute the solutions of the system.
5x₁ + 7x₂ = 3

Answer 1

Cramer's Rule is a method used to solve systems of linear equations. It involves finding the determinant of the coefficient matrix and the determinants of matrices formed by replacing one column of the coefficient matrix with the constants. In this case, the system of equations is 5x₁ + 7x₂ = 3. To use Cramer's Rule, we need to calculate the determinant of the coefficient matrix and the determinants of matrices formed by replacing the first and second columns with the constants. Finally, we can calculate the values of x₁ and x₂ using Cramer's Rule.

Step-by-step explanation:

Cramer's Rule is a method used to solve systems of linear equations. It involves finding the determinant of the coefficient matrix and the determinants of matrices formed by replacing one column of the coefficient matrix with the constants. In this case, the system of equations is 5x₁ + 7x₂ = 3. To use Cramer's Rule, we need to calculate the determinant of the coefficient matrix and the determinants of matrices formed by replacing the first and second columns with the constants.

1. Co-efficient matrix: 5 7
2. Replacing the first column with constants: 3 7
3. Replacing the second column with constants: 5 3

The determinant of the coefficient matrix is 5*7 - 7*0 = 35. The determinant of the matrix formed by replacing the first column with constants is 3*7 - 7*0 = 21. The determinant of the matrix formed by replacing the second column with constants is 5*3 - 3*7 = -4.

Finally, we can calculate the values of x₁ and x₂ using Cramer's Rule:

x₁ = determinant(matrix formed by replacing the first column with constants) / determinant(coefficeient matrix) = 21 / 35 = 0.6

x₂ = determinant(matrix formed by replacing the second column with constants) / determinant(coefficeient matrix) = -4 / 35 = -0.1143