Java Programming Lab Code

A matrix diagonal transformation method is preferred over minor or cofactor of matrix method while finding determinant of the matrix's size over 3x3. The matrix A is converted into Diagonal matrix D by elementary row operation or reduction and then product of main diagonal elements is called determinant of the matrix A. Read matrix A Convert matrix A into diagonal matrix D by applying Row operation or reduction technique Read Main Diagonal elements from D Determinant = product of Main Diagonal elements Algorithm steps for Determinant by Diagonal matrix Read matrix A a - element of the matrix A i,j - position of a element in the matrix for i=1 To N for j=1 To N if i not-equal j RowOperation .add(j,i ,-a ii /a ji ) end end end Determinant = a 11 x a 22 x ... x a nn Java program for a matrix Determinant by Diagonal matrix public class Determinant { Matrix mat; publ...

Determinant, a properties of matrix determines the matrix is singular or not. Lower Triangular matrix transformation method is preferred over minor or cofactor of matrix method while finding determinant of the matrix's size over 3x3. The matrix A is converted into Lower triangular matrix, L by elementary row operation or reduction and then product of main diagonal elements is called determinant of the matrix A. Read matrix A Convert matrix A into L by applying Row operation or reduction technique Read Main Diagonal elements from L Determinant = product of Main Diagonal elements Algorithm steps for Determinant by Lower Triangular Matrix Read matrix A a - elements of matrix A i,j - position of a element in the matrix for i=N-1 To 1 decrement by -1 for j=i-1 To 1 decrement by -1 RowOperation.add(j,i ,-a ii /a ji ) end end Determinant = a 11 x a 22 x ... x a nn Java progr...

Determinant, a properties of matrix determines the matrix is singular or not. Upper triangular method is preferred over minor or cofactor of matrix method while finding determinant of the matrix's size over 3x3. The matrix A is converted into upper triangular matrix U by elementary row operation and then multiplication of main diagonal elements is called determinant of the matrix A. Read matrix A Convert matrix A into U by applying Row operation Read Main Diagonal elements from U Determinant = product of Main Diagonal elements Algorithm steps for Determinant by Upper Triangular Matrix Read matrix A a - element of the matrix A i,j - position of a element in the matrix for i=1 To N for j=i+1 To N RowOperation.add (j,i ,-a ii /a ji ) end end Determinant = a 11 x a 22 x ... x a nn Java program for Determinant by Upper Triangular Matrix...