Linear Algebra Examples

${1, 2, 3, 4, 5, 6, 7}$

Step 1

The power set of a set $S$ is the set of all subsets of $S$ . The first subset will be set $S$ itself. Next, find all subsets that contain one less element (in this case $6$ elements). Continue with this process until finding all subsets including the empty set.

Power Set = ${{1, 2, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 7}, {2, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 6}, {1, 2, 3, 4, 7}, {1, 2, 3, 5, 6}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 6}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 6}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}, {2, 3, 4, 5, 6}, {2, 3, 4, 5, 7}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}, {2, 4, 5, 6, 7}, {3, 4, 5, 6, 7}, {1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 3, 6}, {1, 2, 3, 7}, {1, 2, 4, 5}, {1, 2, 4, 6}, {1, 2, 4, 7}, {1, 2, 5, 6}, {1, 2, 5, 7}, {1, 2, 6, 7}, {1, 3, 4, 5}, {1, 3, 4, 6}, {1, 3, 4, 7}, {1, 3, 5, 6}, {1, 3, 5, 7}, {1, 3, 6, 7}, {1, 4, 5, 6}, {1, 4, 5, 7}, {1, 4, 6, 7}, {1, 5, 6, 7}, {2, 3, 4, 5}, {2, 3, 4, 6}, {2, 3, 4, 7}, {2, 3, 5, 6}, {2, 3, 5, 7}, {2, 3, 6, 7}, {2, 4, 5, 6}, {2, 4, 5, 7}, {2, 4, 6, 7}, {2, 5, 6, 7}, {3, 4, 5, 6}, {3, 4, 5, 7}, {3, 4, 6, 7}, {3, 5, 6, 7}, {4, 5, 6, 7}, {1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 2, 6}, {1, 2, 7}, {1, 3, 4}, {1, 3, 5}, {1, 3, 6}, {1, 3, 7}, {1, 4, 5}, {1, 4, 6}, {1, 4, 7}, {1, 5, 6}, {1, 5, 7}, {1, 6, 7}, {2, 3, 4}, {2, 3, 5}, {2, 3, 6}, {2, 3, 7}, {2, 4, 5}, {2, 4, 6}, {2, 4, 7}, {2, 5, 6}, {2, 5, 7}, {2, 6, 7}, {3, 4, 5}, {3, 4, 6}, {3, 4, 7}, {3, 5, 6}, {3, 5, 7}, {3, 6, 7}, {4, 5, 6}, {4, 5, 7}, {4, 6, 7}, {5, 6, 7}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {1, 7}, {2, 3}, {2, 4}, {2, 5}, {2, 6}, {2, 7}, {3, 4}, {3, 5}, {3, 6}, {3, 7}, {4, 5}, {4, 6}, {4, 7}, {5, 6}, {5, 7}, {6, 7}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {}}$