Solve the following: Show the matrix` [[x+y,y+z,z+x],[1,1,1],[z,x,y]]` is a singular

Solve the following equations by the method of inversion: x+y+z = -1 , x-y+z = 2 and x+y-z = 3 .

Find the inverse of the matrix: [[1,2,3],[2,4,5],[3,5,6]] . Hence solve the equations x+2y+3z = 2 , 2x+4y+5z = 1 , 3x+5y+6z = 3 .

Solve the following equations by the method of inversion: 5x-y+4z = 5 , 2x+3y+5z = 2 and 5x-2y+6z = -1 .