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- A map with 5 dots. A is connected to B, B is connected to C, C is connected to D and E, and D and E are connected to each other
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-\tikz{\node[shape=circle,draw=black] (A) at (0,0) {A};
- \node[shape=circle,draw=black] (B) at (0,2) {B};
- \node[shape=circle,draw=black] (C) at (0,4) {C};
- \node[shape=circle,draw=black] (D) at (-2,6) {D};
- \node[shape=circle,draw=black] (E) at (2,6) {E};
- \draw (A)--(B)--(C)--(D)--(E)--(C)}
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Use the included map in this problem.
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Adjacency map, showing roads between 5 cities
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+ A map with 5 dots. A is connected to B, B is connected to C, C is connected to D and E, and D and E are connected to each other
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An adjacency matrix for this map is a matrix that has the number of roads from city i to city j in the (i,j) entry of the matrix. A road is a path of length exactly 1. All (i,i)entries are 0. Write the adjacency matrix for this map, with the cities in alphabetical order.
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What does the square of this matrix tell you about the map? The cube? The n-th power?
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What does the square of this matrix tell you about the map? The cube? The n-th power?
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diff --git a/source/linear-algebra/source/04-MX/prefigure/MX1-adjacency-graph.xml b/source/linear-algebra/source/04-MX/prefigure/MX1-adjacency-graph.xml
new file mode 100644
index 000000000..4cac2746f
--- /dev/null
+++ b/source/linear-algebra/source/04-MX/prefigure/MX1-adjacency-graph.xml
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\ No newline at end of file