Please solve 4.66. The definition and collary is to help answer problem. Thank you! Problem 4.66. Compute the number of blocks containing each individual point in a finite projec-tive plane build over Fq. Definition 4.15. A basis is a spanning set of minimum size in a vector space. Normally, basesare not ordered. An ordered basis for a vector space is a basis with the members of the basispresented in a particular order.Lemma 4.15. Let F, be a finite field with q elements. Then the vector space F" hasn-1II" – g*)k=0ordered bases.Proof:We count the ordered bases by selected the members of the basis in order. There are q" vectors invector space, one of which is the zero vector. The first member of the ordered basis is one of theqn – 1 non-zero vectors. This vector generates a one-dimensional subspace containing q vectors.The second element is chosen from outside of this subspace, giving us q" – q choices. In generalthe first k vectors chosen span a subspace of size qk leaving q" – qk choices for the next vector inthe basis. The basis must have n elements and the choices made are, other than the constraintof being outside of the subspace already covered, independent, and so they multiply. The formulagiven in the lemma follows. OCorollary 12. Adopt the situation in Lemma 4.15. There areт-1II (7" – *)k=0ordered bases for m-dimensional subspaces of F".Proof:The corollary follows because it simply stops the basis selection process early. O

Let the number of k dimensional subspaces of an n dimensional vector space over a field with q…

Answered: Problem 4.66. Compute the number of…

Problem 4.66. Compute the number of blocks containing each individual point in a finite projec- tive plane build over Fg.

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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