QuestionQuestion

Part I
3. Let A be a (0,1)-matrix of order n satisfying the equation A + Aᵀ = J - I. Prove that the term rank of A is at least n - 1.
7. Prove that the product of two doubly stochastic matrices is a doubly stochastic matrix.
8. Let A be a doubly stochastic matrix of order n. Let A' be a matrix of order n - 1 obtained by deleting the row and column of a positive element of A. Prove that per(A) > 0.

Part II
2. Show that the n eigenvalues of the matrix tI - aJ of order n are t with multiplicity n - 1 and t + an
4. Let A be a (0,1)-matrix of order n which satisfies the matrix equation AAᵀ = tI - aJ. Generalize the argument given in the text for a = 1 to prove that A is a normal matrix.
6. Verify that the incidence matrix A of the projective plane of order 2 satisfies per(A) = |det(A)| = 24.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution.pdf.

    $38.00
    for this solution

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Combinatorics Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats