Linear Algebra and the C Language/a06v

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c00g.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ void fun(int r) { int c1 = C1; int c2 = C2; double **A = r_mR( i_mR(r,r),9.); double **B = swapC_mR(c_mR(A, i_mR(r,r)),c1,c2) ; 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 columns (c[%d],c[%d]) are interchanged\n",c1,c2); 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 columns, the determinant changes sign. Screen output example: A: -2 +6 -3 +4 +8 -2 -8 +1 -6 B: +6 -2 -3 +8 +4 -2 +1 -8 -6 If B is the matrix that results when two columns (c[1],c[2]) are interchanged then : det(B) = - det(A) det_R(A) = +128 det_R(B) = -128 Press return to continue Press X return to stop