--- title: "Add and subtract matrices in FORTRAN" subject: "Computer Programming" chapter: 11 key: "semester_1/computer_programming:fortran-matrix-add-subtract" source: https://www.bctengineer.com/q/semester_1/computer_programming/fortran-matrix-add-subtract site: BCT Engineering --- # Add and subtract matrices in FORTRAN Computer Programming · Chapter 11: Programming Language: FORTRAN - Asked in: 2072 Chaitra, 7 marks - Video: [Matrix Addition, Subtraction & Multiplication | FORTRAN](https://www.youtube.com/watch?v=TIfwcv2PWGs) — Bisank's Ultimate Guide - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_1/computer_programming/fortran-matrix-add-subtract - Whole chapter: https://www.bctengineer.com/md/semester_1/computer_programming/chapter-11 ## Question Write a FORTRAN program to add and subtract two matrices and display the results in matrix form. ## Short answer Read rows, columns, and matrices using nested implied DO. Compute sum S(i,j)=A(i,j)+B(i,j) and difference D(i,j)=A(i,j)-B(i,j) in loops. Display each matrix row by row with FORMAT. For A=[1 2;3 4], B=[5 6;7 8], sum is [6 8;10 12] and difference [-4 -4;-4 -4]. ## Answer **Method.** Matrices of the same order r × c are read row by row with a nested implied DO. The sum is S(i,j) = A(i,j) + B(i,j) and the difference is D(i,j) = A(i,j) − B(i,j). Each result is printed one row per line using a FORMAT statement. ```fortran PROGRAM MATADS INTEGER A(10,10), B(10,10), S(10,10), D(10,10) INTEGER R, C, I, J PRINT *, 'ENTER ROWS AND COLUMNS' READ *, R, C PRINT *, 'ENTER FIRST MATRIX' READ *, ((A(I,J), J = 1, C), I = 1, R) PRINT *, 'ENTER SECOND MATRIX' READ *, ((B(I,J), J = 1, C), I = 1, R) DO 20 I = 1, R DO 10 J = 1, C S(I,J) = A(I,J) + B(I,J) D(I,J) = A(I,J) - B(I,J) 10 CONTINUE 20 CONTINUE PRINT *, 'SUM OF THE MATRICES' DO 30 I = 1, R WRITE(*,100) (S(I,J), J = 1, C) 30 CONTINUE PRINT *, 'DIFFERENCE OF THE MATRICES' DO 40 I = 1, R WRITE(*,100) (D(I,J), J = 1, C) 40 CONTINUE 100 FORMAT(10I5) STOP END ``` **Sample:** for A = [1 2; 3 4] and B = [5 6; 7 8], the sum is [6 8; 10 12] and the difference is [-4 -4; -4 -4]. Note that in `READ *, ((A(I,J), J=1,C), I=1,R)` the elements are typed row by row. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What condition must the two matrices satisfy? A. The same order r x c B. Square matrices only C. Different orders D. The first has fewer rows Answer: A. Addition and subtraction are element by element, so both matrices must have the same order. (Key point: Condition for addition) 2. Which formulas give the sum and difference? A. S(i,j) = A(i,j) * B(i,j); D = A / B B. S(i,j) = A(i,j) + B(i,j); D(i,j) = A(i,j) - B(i,j) C. S(i,j) = A(j,i) + B(i,j) D. S(i,j) = A(i,j) + B(j,i) Answer: B. Corresponding elements are added or subtracted. (Key point: Element formulas) 3. In READ *, ((A(I,J), J=1,C), I=1,R), in what order is the data typed? A. Column by column B. Row by row C. Diagonal first D. Random order Answer: B. The inner variable J varies fastest, so the elements of row 1 are entered first, then row 2. (Key point: Reading order) 4. For A = [1 2; 3 4] and B = [5 6; 7 8], what is A - B? A. [4 4; 4 4] B. [-4 -4; -4 -4] C. [6 8; 10 12] D. [-1 -1; -1 -1] Answer: B. Each element is 4 less than the corresponding element of B, giving -4 everywhere. 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