Linear Algebra and the C Language/a09b

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c00b.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ /* ------------------------------------ */ #define RB R3 #define CB C2 #define RU R2 #define CU C1 /* ------------------------------------ */ /* ------------------------------------ */ int main(void) { double bu_s[RB*(CB+CU)]={ +2, 2, 6, +2, 0, 14, +6, 2, 34, }; double **Bu_s = ca_A_mR(bu_s,i_Abr_Ac_bc_mR(RB,CB,CU)); double **B = c_Ab_A_mR(Bu_s,i_mR(RB,CB)); double **U_s = c_Ab_b_mR(Bu_s,i_mR(RB,CU)); clrscrn(); printf(" B is the change of basis matrix for \"B\" \n\n" " Find the coordinate of U in the \"B\" basis.\n\n" " B : "); p_mR(B,S6,P2,C7); printf( " U_s : The coordinate of U in the Standard basis"); p_mR(U_s,S6,P2,C7); stop(); clrscrn(); printf(" B: "); p_mR(B,S6,P2,C7); printf( " U_s:"); p_mR(U_s,S6,P2,C7); printf("The system B|u_s:"); p_mR(Bu_s,S6,P2,C7); printf(" B|u_s : gj_PP_mR(Ab,YES):"); gj_PP_mR(Bu_s,YES); p_mR(Bu_s,S6,P2,C7); stop(); clrscrn(); printf(" B|u_s :"); p_mR(Bu_s,S6,P2,C7); printf( " U_s : The coordinate of U in the Standard basis"); p_mR(U_s,S6,P2,C7); printf(" U_b : The coordinate of U in the \"B\" basis\n" " %+.2f\n %+.2f\n\n", Bu_s[R1][C3],Bu_s[R2][C3]); stop(); f_mR(Bu_s); f_mR(U_s); f_mR(B); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ The coordinates of U in standard basis: B U_b = U_s (*) b) Find the coordinates of U in basis B: You must create the system and resolve it: You have (*): B U_b = U_s (B: non-invertible matrix) You must resolve the system: B|U_s (Give U in base b: U_b) Screen output example: B is the change of basis matrix for "B" Find the coordinate of U in the "B" basis. B : +2.00 +2.00 +2.00 +0.00 +6.00 +2.00 U_s : The coordinate of U in the Standard basis +6.00 +14.00 +34.00 Press return to continue. B: +2.00 +2.00 +2.00 +0.00 +6.00 +2.00 U_s: +6.00 +14.00 +34.00 The system B|u_s: +2.00 +2.00 +6.00 +2.00 +0.00 +14.00 +6.00 +2.00 +34.00 B|u_s : gj_PP_mR(Ab,YES): +1.00 +0.00 +7.00 +0.00 +1.00 -4.00 +0.00 +0.00 +0.00 Press return to continue. B|u_s : +1.00 +0.00 +7.00 +0.00 +1.00 -4.00 +0.00 +0.00 +0.00 U_s : The coordinate of U in the Standard basis +6.00 +14.00 +34.00 U_b : The coordinate of U in the "B" basis +7.00 -4.00 Press return to continue.