A=rand(5,3) A = 0.9501 0.7621 0.6154 0.2311 0.4565 0.7919 0.6068 0.0185 0.9218 0.4860 0.8214 0.7382 0.8913 0.4447 0.1763 A(:,3)=pi*A(:,1)+exp(1)*A(:,2) A = 0.9501 0.7621 5.0565 0.2311 0.4565 1.9670 0.6068 0.0185 1.9568 0.4860 0.8214 3.7596 0.8913 0.4447 4.0089 [Q,R]=qr(A) Q = -0.6191 -0.1406 0.6953 0.3167 -0.1148 -0.1506 -0.4084 0.1957 -0.8747 0.0842 -0.3954 0.5564 -0.2078 -0.2991 -0.6335 -0.3167 -0.6676 -0.5633 0.2110 -0.3036 -0.5808 0.2410 -0.3433 -0.0222 0.6973 R = -1.5346 -1.0663 -7.7197 0 -0.7245 -1.9695 0 0 -0.0000 0 0 0 0 0 0 format short e R R = -1.5346e+000 -1.0663e+000 -7.7197e+000 0 -7.2452e-001 -1.9695e+000 0 0 -1.0880e-015 0 0 0 0 0 0 b=rand(5,1) b = 4.0571e-001 9.3547e-001 9.1690e-001 4.1027e-001 8.9365e-001 c=Q'*b c = -1.4036e+000 1.2604e-002 -2.6331e-001 -8.9733e-001 -5.0021e-002 R11=R(1:3,1:3) R11 = -1.5346e+000 -1.0663e+000 -7.7197e+000 0 -7.2452e-001 -1.9695e+000 0 0 -1.0880e-015 c1=c(1:3) c1 = -1.4036e+000 1.2604e-002 -2.6331e-001 x=R11\c1 x = -7.6033e+014 -6.5788e+014 2.4202e+014 norm(A*x-b) ans = 8.8407e-001 xrand=rand(3,1) xrand = 5.7891e-002 3.5287e-001 8.1317e-001 norm(A*xrand-b) ans = 5.7338e+000 x x = -7.6033e+014 -6.5788e+014 2.4202e+014 R11=R(1:2,1:2) R11 = -1.5346e+000 -1.0663e+000 0 -7.2452e-001 c1=c(1:2) c1 = -1.4036e+000 1.2604e-002 xreg=R11\c1 xreg = 9.2673e-001 -1.7396e-002 norm(A*xreg-b) ??? Error using ==> mtimes Inner matrix dimensions must agree. norm(A*[xreg; 0] -b) ans = 9.3650e-001 diary off