# Linear Algebra — Finding The Inverse

We are asked to find the inverse of the following matrix, provided the inverse exists: $$\left[\begin{array}{rrr} 1 & a & b+c\\ 1 & b & a+c\\ 1 & c & a+b \end{array}\right]$$

I cannot seem to arrive at any definitive solution. What I do know is that we augment the matrix with the identity matrix and perform elementary row operations such as addition, subtraction and multiplication.

Hint: $a_{i3} = (a+b+c)a_{i1}-a_{i2}$.
• @user4640007: Columns are not linearly independent, hence $\det=0$, inverse does not exist. – g.kov Apr 11 '15 at 6:37