Solve[{0.5 x1 - x2 == -1.5, 
        0.45 x1 - x2 == -1.55}, {x1, x2}]

<< Statistics`Master`

Lose uvjetovan sustav

m = 1000;
a = {{0.5, -1}, {0.45, -1}}; 
    Norm[a, 2]*Norm[Inverse[a], 2]
rjesenje = Table[0, {i, m}];
pogreskeb = 
        Table[{Random[NormalDistribution[0, 0.05]], 
            Random[NormalDistribution[0, 0.05]]}, {i, 
            m}];
Table[
        rj = Solve[{0.5 x1 - x2 == -1.5 + pogreskeb[[i, 1]], 
              0.45 x1 - x2 == -1.55 + pogreskeb[[i, 2]]}, {x1, 
              x2}]; 
rjesenje[[i]] = {First[x1 /. rj], 
            First[x2 /. rj]}, {i, m}];
ListPlot[pogreskeb, PlotStyle -> {Hue[0], PointSize[0.01]}, 
      AspectRatio -> Automatic]
ListPlot[rjesenje, PlotStyle -> {Hue[0.5], PointSize[0.01]}, 
      AspectRatio -> Automatic]

Dobro uvjetovan  sustav

m = 1000;
a = {{4, -1}, {1, 4}}; 
    Norm[a, 2]*Norm[Inverse[a], 2]
rjesenje = Table[0, {i, m}];
pogreskeb = 
        Table[{Random[NormalDistribution[0, 0.05]], 
            Random[NormalDistribution[0, 0.05]]}, {i, 
            m}];
Table[
        rj = Solve[{4  x1 - x2 == 2 + pogreskeb[[i, 1]],  
              x1 + 4  x2 == 9 + pogreskeb[[i, 2]]}, {x1, 
              x2}]; 
rjesenje[[i]] = {First[x1 /. rj], 
            First[x2 /. rj]}, {i, m}];
ListPlot[pogreskeb, PlotStyle -> {Hue[1], PointSize[0.01]}, 
      AspectRatio -> Automatic]
ListPlot[rjesenje, PlotStyle -> {Hue[0.5], PointSize[0.01]}, 
      AspectRatio -> Automatic]

Hilbertova matrica

n = 5;
h = 
        Table[1/(i + j - 1), {i, n}, {j, 
            n}];
MatrixForm[h]
cond = Norm[h, 2]*Norm[Inverse[h], 2] // N

prikaz = 
        Table[h = Table[1/(i + j - 1), {i, n}, {j, n}]; {n, 
            Log[Norm[h, 2]*Norm[Inverse[h], 2] // N]}, {n, 1, 
            15}];
ListPlot[prikaz, 
        PlotStyle -> {Hue[1], 
            PointSize[0.02]}];
SingularValues[N[h]]