Question

Write condition on coefficient matrix a for solving simultaneous system of equations by cholesky method. Section – b (short answer questions)

Answer 1

Answer:

The cholesky decomposition method is the procedure which can be use to solve the simultaneous system of equations.

It can be use when coefficient matrix A of the system of simultaneous  equations is square conjugate symmetric matrix.

And we Know that

According to the definition of conjugate symmetric matrix.

"The matrix A is called conjugate symmetric matrix if

                           Ajk is equal to Akj conjugate that is

                          Ajk= Akj °     where Akj ° indicate the complex conjugate."

We know that when symmetric matrix A have real entries then the conjugate of Ajk is equal to Akj that is

                          Ajk = Akj.

SO when matrix A is symmetric matrix with real entries we use cholesky decomposition method to solve the system of simultaneous equation.

(Note: Ajk denote the entries in jth rows and kth columns )