Definition:
Cramer's rule is a method for solving a system of linear equations in 3 variables using determinants.
Solutions by Cramer's rule:
- Cramer's rule is a method for solving a system of linear equations using determinants.
- Cramer's rule involves calculating the determinants of matrices obtained by replacing the coefficient matrix with column vectors of constants.
- The solution of the system of equations is obtained by dividing the determinant of each matrix by the determinant of the coefficient matrix.
- Cramer's rule can be used to find the solution of a system of linear equations in any number of variables.
- Cramer's rule is computationally expensive and is not suitable for solving systems of equations with a large number of variables.
Important Formulas to Remember in these topic Solutions by Crammer‘s rule:
- Let A be the coefficient matrix and B be the constant matrix, then $$x = \frac{|X|}{|A|},\quad y = \frac{|Y|}{|A|},\quad z = \frac{|Z|}{|A|}$$ where X, Y, and Z are the matrices obtained by replacing the respective column of A with B and |A|, |X|, |Y|, and |Z| are the determinants of A, X, Y, and Z, respectively.