Linear Algebra and the C Language/a06w

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c00h.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ void fun(int r) { int r1 = R1; int r2 = R2; double **A = r_mR( i_mR(r,r),9.); double **B = swapR_mR(c_mR(A, i_mR(r,r)),r1,r2) ; clrscrn(); printf(" A:"); p_mR(A, S3,P0,C6); printf(" B:"); p_mR(B, S3,P0,C6); printf(" If B is the matrix that results when \n"); printf(" two rows (r[%d],r[%d]) are interchanged\n",r1,r2); printf(" then : det(B) = - det(A)\n\n\n"); printf(" det_R(A) = %+.0f\n", det_R(A)); printf(" det_R(B) = %+.0f\n", det_R(B)); f_mR(A); f_mR(B); } /* ------------------------------------ */ int main(void) { time_t t; srand(time(&t)); do { fun(rp_I(RC4)+RC1); } while(stop_w()); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ We can verify numerically that if we swap two rows, the determinant changes sign. Screen output example: A: -7 -9 -4 -7 +1 +4 +9 -5 -1 +9 +7 -3 +6 +4 -9 +9 B: -7 -9 -4 -7 -1 +9 +7 -3 +1 +4 +9 -5 +6 +4 -9 +9 If B is the matrix that results when two rows (r[2],r[3]) are interchanged then : det(B) = - det(A) det_R(A) = -2765 det_R(B) = +2765 Press return to continue Press X return to stop