Question

The inverse of a diagonal matrix is also a diagonal matrix if all the diagonal entries are non-zero. 1. True, because the inverse of each non-zero diagonal entry will still result in a diagonal matrix. 2. False, the inverse of a diagonal matrix can sometimes be a non-diagonal matrix. 3. True, only if the matrix is square. 4. False, diagonal matrices cannot have an inverse. 5. None of the above.

Name: the inverse of a diagonal matrix is also a diagonal matrix if all the diagonal entries are non zero 1 true because the inverse of each non zero diagonal entry will still result in a diagonal 96883
Uploaded: 2023-01-03T02:41:31-08:00
Duration: 2 min 16 s
Channel: Vincenzo Zaccaro
Description: the inverse of a diagonal matrix is also a diagonal matrix if all the diagonal entries are non zero 1 true because the inverse of each non zero diagonal entry will still result in a diagonal 96883

          The inverse of a diagonal matrix is also a diagonal matrix if all the diagonal entries are non-zero.
1. True, because the inverse of each non-zero diagonal entry will still result in a diagonal matrix.
2. False, the inverse of a diagonal matrix can sometimes be a non-diagonal matrix.
3. True, only if the matrix is square.
4. False, diagonal matrices cannot have an inverse.
5. None of the above.

Added by Shawn B.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Vincenzo Zaccaro

01/03/2023

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The inverse of a diagonal matrix is also a diagonal matrix if all the diagonal entries are non-zero. 1. True, because the inverse of each non-zero diagonal entry will still result in a diagonal matrix. 2. False, the inverse of a diagonal matrix can sometimes be a non-diagonal matrix. 3. True, only if the matrix is square. 4. False, diagonal matrices cannot have an inverse. 5. None of the above.