Question 870839
a) the determinant of a two by two matrix is (ad - bc)
we have (x-1)^2 - (-2)(x-2) = x^2 -2x +1 +2x -4 = x^2 -3
we want the determinant to be 0, so x^2 -3 = 0 and x = square root (3)
b) these are adjacency matrices for diagraphs, to do a diagraph number the vertices of an adjacencey matrix from 1 to n.  Each element Aij is 1 if there is an arc from vertex i to j and Aij = 0 if there is no arc from i to j.
With this info, you should be able to do the diagraph's for these adjacencey matrices.