Transcribed TextTranscribed Text

Let U denote the vector space of continuous functions on the interval (0, xo), i.e. U={f:(0,xo) R I f is continuous}. For every a > 0 define the linear operator Ta : U U by Ta(f(x)) = f(ax). (a) Show that To o Tb = Tab- (b) Let W = span{1, x, In(x), . In(x) }. Show that Ta sends vectors in W into vectors in W and write the matrix [TalB of T in the basis B = {1, x, In(x), T In(x) 1. * (c) Find the inverse of the matrĂ­x [Ta]B from (b). I P6 Let A be a 7 X 7-matrix with characteristic polynomial EA (t) = - _t3 (t+3) (t-1) - (t-5) (t-6). (a) Show that the rank of A equals 4, 5, or 6. (b) Assume that the rank of A equals 4. Is A diagonalizable? Explain!

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:

    for this solution

    or FREE if you
    register a new account!

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

    Find A Tutor

    View available Linear Algebra 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.

    Upload a file
    Continue without uploading

    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