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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)

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