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FORTRAN 90 Lecturer : Rafel Hekmat Hameed University of Babylon Subject : Fortran 90 College of Engineering Year : Second B.Sc. Mechanical Engineering Dep. Determinants Every square matrix has a value called a determinant,, and only square matrices ices have defined determinants. The determinant of a 2x2 square matrix is the difference of the products of the diagonals. The "down"" diagonal is in red and the "up" " " diagonal is in blue. The up diagonals are always subtracted from the down diagonals. Matrices that are larger than a 2 x 2 matrix become a little more complicated when finding the determinant but the same rules apply. Let's find When finding the determinant of a 3 x 3 matrix it is helpful to write the first two columns to the right side of the matrix like so ϭ A fortran 90 program to find the determinant of 33 matrix. Program determinant ; implicit none Integer, parameter::n=3, m=5 Integer, dimension (n,m):: a ; Integer:: i, j, det1, det2, det Read(*,*) ((a(I,j),j=1,n),i=1,n) Do i=1,n ; do j=1,n-1 a(i,n+j)=a(I,j) ; do i=1,n enddo ; ;det1=1 enddo ; det2=1 do j=1,n det1=det1*a(j,i+j-1) ; det2=det2*a(j,2*n-j-i+1) det=det+det1-det2 enddo ; write(*,6) "determinant=", det ;6 format(2x,a,2x,i8); ;enddo end If the matrix has more than three columns, then the determinant be determined, as illustrated by example below A= ͵ ቚ Ͷ ተ͵ Det A = ቚ ተ͵ ͵ ቚ ͷ ͵ ቚ ቚ Ͷ ͵ ቚ ቚ ͳ ͵ ͵ ቚ ቚ ʹ ͷ െ͵ ቚ െͳͷ ቮ െ͵ ቚ െʹͶ 3 4 3 5 ͺ ͵ ቚ ቚ Ͷ ͺ ͵ ቚ ቚ ͷ ͵ ͺ ͵ ቚ ቚ Ͷ ͷ െͳͳ െ͵ ቚ ቚ െͻ െͳͷ െͳͳ െ͵ ቚ ቚ െʹͺ െʹͶ 6 7 1 2 8 7 5 4 6 7 2 3 ቚ െ͵ െͳͳ െ͵ ተ ቚ ֜ อെͳͷ െͻ െͳʹอ ֜ ʹተ െʹͶ െʹͺ െʹͳ ቚ ͵ െ͵ ቚ െͳʹ ቮ ֜ ቚെͳ͵ͺ െ͵ െͳͺͲ ቚ െʹͳ Det A= (-138*-9) – ( -180*-9) = -378 Ϯ െͻ ቚ ֜ െͻ ܣ ฬ ଵଵ ܣଶଵ ተܣ ฬ ଵଵ ܣ ተ ଷଵ ܣ ฬ ଵଵ ܣସଵ ܣଵଶ ฬ ܣଶଶ ܣଵଶ ฬ ܣଷଶ ܣଵଶ ฬ ܣସଶ ܣଵଷ ܣ ฬ ฬ ଵଵ ܣଶଷ ܣଶଵ ܣଵଷ ܣ ฬ ฬ ଵଵ ܣଷଷ ܣଷଵ ܣଵଷ ܣ ฬ ฬ ଵଵ ܣସଷ ܣସଵ ܣ ฬ ଵଵ ܣଶଵ ܣ ฬ ଵଵ ܣଷଵ ܣ ฬ ଵଵ ܣସଵ IMPLICIT NONE INTEGER ,DIMENSION (4,4)::A INTEGER,DIMENSION (1:3,1:3)::B INTEGER::I, J, N DATA A/3,4,3,5,6,7,1,2,8,7,5,4,6,7,2,3/ DO N=4, 2 ,-1 DO I=1, N-1 DO J=1,N-1 B(I,J)=A(1,1)*A(I+1,J+1)-A(1,J+1)*A(I+1,1) ENDDO ; ENDDO DO I=1,N-1 DO J=1,N-1 A(I,J)=B(I,J) ENDDO;ENDDO DO I=1,N-1 PRINT*,(B(I,J),J=1,N-1) ENDDO PRINT *, ' ******************************************* ' ENDDO END ϯ ܣଵସ ฬ ܣଶସ ܣଵସ ተ ฬ ܣଷସ ተ ܣଵସ ฬ ܣସସ Singular and Non-Singular Singular Matrices An n square matrix A is called singular if det A=0 ; if det A ##0, A is called non-singular. Example Given that Determine whether this matrix is singular or non-singular. non Solution Therefore, matrix A is singuular ϰ
