CPI 200
MockFinal not graded
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A =(({{1, 1, 1}, {1, 0, 0}, {0, 1, 1}})),  v=(({{2}, {0}, {-2}}))

1.  Is v an eigenvector of A? Explain. (No points w/o expanation)

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

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

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

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

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

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

4. Find the column normalized form of A.

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

5.  Find det A

0, since two columns are identical.

6. Are the three vectors (1,2,3), (-1,2,3), (0,4,6) linearly independent? Explain.

No. The last two columns are the same.

7. Let C=(({{-1, 0}, {0, -4}})). Find (C^(-1))

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

8. Find a 2x2 matrix which reflects all 2D vectors across the y-axis.

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