What is Cramer's Rule?

1 Answer
Nov 12, 2015

Answer:

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#.