Q02 (4 points) Let P be the set of 1-dimensional linear subspaces of V = F2,...

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Q02 (4 points) Let P be the set of 1-dimensional linear subspaces of V = F2, and let L be the set of 2-dimensional linear subspaces of V. We will call the elements of P "points" and the elements of L "lines". We say that a point p E P and a line l € L are incident when p is a subspace of 1. Choose a labeling of the points (P₁, P2,...) and a labeling of the lines (11, 12,...). Write the 7 x 7 incidence matrix M = [mij], where mij is 1 if p; is incident to l; and 0 otherwise. How many points are incident to each line? How many lines are incident to each point? Can you explain this? Not to be handed in: Is it possible to label the points and lines in the previous question in such a way that the matrix M is symmetric, i.e. mij = mji? Q02 (4 points) Let P be the set of 1-dimensional linear subspaces of V = F2, and let L be the set of 2-dimensional linear subspaces of V. We will call the elements of P "points" and the elements of L "lines". We say that a point p E P and a line l € L are incident when p is a subspace of 1. Choose a labeling of the points (P₁, P2,...) and a labeling of the lines (11, 12,...). Write the 7 x 7 incidence matrix M = [mij], where mij is 1 if p; is incident to l; and 0 otherwise. How many points are incident to each line? How many lines are incident to each point? Can you explain this? Not to be handed in: Is it possible to label the points and lines in the previous question in such a way that the matrix M is symmetric, i.e. mij = mji?

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Solutions 3 Given that p be the set of 1di ... View the full answer