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Cramer's Rule Explained

Determinant of a 2x2 Matrix:    • How to find the Determinant of a 2x2 ...   Determinant of a 3x3 Matrix:    • Determinant of a 3x3 Matrix   Cramers Rule Cramer's rule is invented by mathematician Gabriel Cramer in 1750s. This rule is used to find the solution of a system of equations with any number of variables and the same number of equations. Sometimes, when we are solving a system of equations in 3 variables, say x, y, and z, we may need to solve for two variables x and y to solve for variable z. But using Cramer's rule, we can find the value of any variable without finding the values of the other variables. But this rule has some limitations with respect to the solutions. This rule can be applied only when the system has unique solutions. But how do we know when a system has unique solution? Let us learn more about this along with the definition and formula of Cramer's Rule. What is Cramer's Rule? Cramer's rule is one of the methods used to solve a system of equations. This rule involves determinants. i.e., the values of the variables in the system are found with the help of determinants. Let us consider a system of equations in n variables x₁, x₂, x₃, ..., xₙ written in the matrix form AX = B, where A = the coefficient matrix which is a square matrix X = the column matrix with variables B = the column matrix with the constants (which are on the right side of the equations)