SOLUTION: Could you please help me to understand this q step by step? find the x value of the 2x2 matrix that make the determinant zero? ( Linear Algebra Q) x-1 -2 x-2 x-1 also i

Question 870839: Could you please help me to understand this q step by step?
find the x value of the 2x2 matrix that make the determinant zero?
( Linear Algebra Q)
x-1 -2
x-2 x-1

also i'm unable to understand how to sketch a digraph? of matrices
its so confusing
1)
0 1 1 0
0 0 1 1
0 0 0 1
1 0 0 0
2)
0 1 1 0
1 0 1 0
1 1 0 0
3)
0 1 0 1 0
1 0 1 0 0
0 1 0 1 0
1 0 0 0 0
1 1 1 1 0

please help me through simipifying the answers so that i'd understand
im using Linear algebra with application 5th edition by gareth williams
the text book doesnt show any other examples of how to sketch.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
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.

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