Explanation:

Cramer's rule is a technique used to solve a system of linear equations by using determinants. It is named after the Swiss mathematician Gabriel Cramer. The rule is based on the concept of determinants of matrices and provides a method for solving a system of linear equations using determinants.

Cramer's Rule is also known as Determinant Method because it involves the calculation of determinants to find the solution to a system of linear equations.

Cramer's Rule involves the following steps:

1. Write the system of linear equations in matrix form.

2. Calculate the determinant of the coefficient matrix.

3. Replace each column of the coefficient matrix with the column of constants and calculate the determinant of the resulting matrix for each column.

4. Divide each determinant obtained in step 3 by the determinant obtained in step 2 to get the values of the variables.

Cramer's Rule is an alternative method to solve a system of linear equations if the coefficient matrix is invertible. It is particularly useful when the number of equations and variables is small.

Conclusion:

Cramer's Rule is a powerful technique for solving a system of linear equations using determinants. It is widely used in mathematics and engineering applications. Cramer's Rule is also known as Determinant Method because it involves the calculation of determinants to find the solution to a system of linear equations.