Mathematics · Abstract Algebra & Vector Spaces
Let &mathbb;Fq be a finite field with q elements. For n ≥ 2, let A be a 2n × 2n matrix with entries in &mathbb;Fq such that rank(A) = n. Let W = {v ∈ &mathbb;Fq2n | Av = 0}. Which of the following represents the number of (n + 2)-dimensional subspaces of &mathbb;Fq2n that contain W?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 11
- 2(q2n - qn)(q2n - qn+1)qn
- 3(q2n - 1)(q2n - q) … (q2n - qn-1)qn
- 4(qn - 1)(qn - q)(q2 - 1)(q2 - q)✓
Correct answer
(qn - 1)(qn - q)(q2 - 1)(q2 - q)
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