Linear Algebra and the C Language/a04h
Install and compile this file in your working directory.

/* ------------------------------------ */
/* Save as: c00b.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define RA R4
#define CA C3
#define Cb C1
/* ------------------------------------ */
#define FACTOR_E +1.E-0
/* ------------------------------------ */
int main(void)
{
double ta[RA*(CA+Cb)]={
/* x1 x3 x4 */
+1, +0, +0,/* A */
+0, +1, +0,/* B */
+0, -1, +1,/* C */
-1, +0, -1 /* D */
};
double tb[RA*(CA+Cb)]={
+20+10, // A
+60 -10 -30, // B
+20, // C
-100+30, // D
};
double **A = ca_A_mR(ta, i_mR(RA,CA));
double **b = ca_A_mR(tb, i_mR(RA,C1));
double **Pinv = Pinv_Rn_mR(A, i_mR(CA,RA),FACTOR_E);
double **x = mul_mR(Pinv,b, i_mR(CA,C1));
clrscrn();
printf(" A:");
p_mR(A, S5,P1,C6);
printf(" b:");
p_mR(b, S5,P1,C6);
printf(" Pinv = V invS_T U_T ");
pE_mR(Pinv, S12,P4,C6);
printf(" x = Pinv b ");
p_mR(x, S10,P4,C6);
stop();
f_mR(b);
f_mR(A);
f_mR(Pinv);
f_mR(x);
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

Screen output example:
A :
+1.0 +0.0 +0.0
+0.0 +1.0 +0.0
+0.0 -1.0 +1.0
-1.0 +0.0 -1.0
b :
+30.0
+20.0
+20.0
-70.0
Pinv = V * invS_T * U_T
+7.5000e-01 -2.5000e-01 -2.5000e-01 -2.5000e-01
-2.5000e-01 +7.5000e-01 -2.5000e-01 -2.5000e-01
-5.0000e-01 +5.0000e-01 +5.0000e-01 -5.0000e-01
x = Pinv * b
+30.0000
+20.0000
+40.0000
Press return to continue.