Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anilorap

  • 4 years ago

find the det(A), where A is a square matrix satisfying the property that A(transpose)A= I

  • This Question is Closed
  1. anilorap
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[A^{t}A=I\]

  2. Zarkon
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    for square matrices DET(AB)=Det(A)Det(B)

  3. Zarkon
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I guess I should add that Det(I)=1 and Det(A)=Det(A^T)

  4. anilorap
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so i have \[\det(A ^{t} A)=\det(I)\] \[\det(A ^{t}) \det(A) =\det(I)\]

  5. Zarkon
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\det(A ^{t}) \det(A) =\det(I)=1\] \[\det(A) \det(A) =1\] \[\det(A)^2=1\] \[\det(A)=\pm\sqrt{1}=\pm1\]

  6. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy