A  =  { {1, 2, 3}, 
        {4, 5, 
          6}, 
        {7, 8, 10}}

b  =  {-1, 0, 1}

Xa  =  N[Inverse[A] . b]

Xb  =  N[LinearSolve[A, b]]

Xb - Xa

MatrixForm[LUDecomposition[A]]

A  =  {{1, 0}, 
       {1, 
          1}, 
       {1, 
          2}, 
       {1, 3}}

MatrixForm[%]

b  =  {{1}, {4}, {5}, {8}}

Aplus  =  PseudoInverse[A]

w  =  Aplus . b