CPI 200
Quiz 7 /  graded
Name:	
ID:

A =(({{1, 0, 1}, {1, 0, 0}, {0, 1, 1}})),  v=(({{2}, {0}, {2}}))

1.  Is v an eigenvector of A? Explain.

	No, since Av is not a multiple of v.

2. For the linear system Ax = v, perform one Gauss elimination step. (zeroing out the (Subscript[a, 2,1]) element)

A =(({{1, 0, 1}, {0, 0, -1}, {0, 1, 1}})),  v=(({{2}, {-2}, {2}}))

3. Find a 3x3 matrix with eigenvalues 1,1,0.

(({{1, 0, 1}, {0, 1, -1}, {0, 0, 0}}))

(*
-y  = 2,
3x +2y= 2
*)
Plot[{1 - 1.5x,-2},{x,0,2},PlotStyle->Thick]
LinearSolve[aa,v]

4.  The matrix A may be interpreted as an adjaceny matrix. Sketch the corresponding graph.

aa={{1,0,1},{1,0,0},{0,1,1}};
AdjacencyGraph[aa,VertexLabels->"Name"]

5. What is a stochastic matrix?

A matrix which each column summing to one.

6. Find the column normalized form of A.

(({{1/2, 0, 1/2}, {1/2, 0, 0}, {0, 1, 1/2}}))

cc={{-1,0},{0,4}};
Print[MatrixForm[Inverse[cc]]]

pp={{1,0},{0,-1}};
Print[MatrixForm[pp]]