SOLUTION: If {{{M}}}{{{""=""}}}{{{(matrix(3,3,1,-1,k,4,7,3,-1,12,-2))}}} Evaluate in term of k the determinant of M. Hence, if {{{X}}}{{{""=""}}}{{{(matrix(3,1,x,y,z))}}}, Solve the equat

The cofactor method of finding the inverse is the hardest way.
Here goes:










In order to solve the equation 



We must find the inverse of M which is written M-1 by the long,
hard, cofactor method:

We replace each element of M by the determinant of its cofactor, which is its
minor 2x2 determinant.



We put in the "checkerboard" of signs, this will be the cofactor matrix



We evaluate the determinants












Next we form the adjoint or adjugate matrix which is the transpose
of the matrix of cofactors:



Now we find the inverse of M by multiplying the adjoint or adjugate
by the reciprocal of the value of the determinant of M. We calculated
the value of the determinant of M in terms of k as

But we were told to use k=2, so substituting,

So we multiply the adjoint or adjugate by 





Next we multiply both sides of the equation we are to solve:



by the inverse M-1:





So



Edwin