Question

What is Cramer's Rule?

Answer 1

It is a rule used to help solve a system of linear equations.

Explanation:

Let `Ax=b` be a linear system of n equations in n unknowns, where `A_(nxxn)` is the coefficient matrix of the system.

Let the determinant of the A be `det(A)=Delta`.

Now replace any column `a_j` of A with the column `b`, the solution set.

Form the new determinant of the new matrix so formed and call it `Delta_(j)`.

Then by Kramer's Rule, the solution value for the variable `x_j` may be given by
`x_j=(Delta_(j))/(Delta)`.

We may repeat this `AA j=1,2,3,....,n`.