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>> A

A =

     1     0     0
     0     0     1
     1     0     1
     1     1     0
     0     1     1

>> [Q,R] = qr(A)

Q =

   -0.5774    0.2582    0.1291   -0.7490    0.1495
         0         0   -0.6455   -0.2549   -0.7200
   -0.5774    0.2582   -0.5164    0.5020    0.2853
   -0.5774   -0.5164    0.3873    0.2470   -0.4347
         0   -0.7746   -0.3873   -0.2470    0.4347


R =

   -1.7321   -0.5774   -0.5774
         0   -1.2910   -0.5164
         0         0   -1.5492
         0         0         0
         0         0         0

>> c = [280;118;400;390;210]

c =

   280
   118
   400
   390
   210

>> d = Q'*c

d =

 -617.7648
 -188.4852
 -176.8662
    5.4506
   -7.2542

>> R0 = R(1:3,1:3)

R0 =

   -1.7321   -0.5774   -0.5774
         0   -1.2910   -0.5164
         0         0   -1.5492


>> d0 = d(1:3)

d0 =

 -617.7648
 -188.4852
 -176.8662

>> R0\d0

ans =

  285.1667
  100.3333
  114.1667

>>