In[1]:=
matrix1={
    {m11, m12,m13, m14},
    {m21,m22,m23,m24},
    {m31,m32,m33,m34},
    {m41,m42,m43,m44}
    }

In[2]:=
MatrixForm[matrix1]

In[3]:=
a={a1,a2,a3,a4}

In[4]:=
LinearSolve[matrix1,a]

In[5]:=
Simplify[%]

In[6]:=
Limit[LinearSolve[matrix1,a],m11 -> Infinity]