A is a 3x3 matrix with two eigenvalues. Each eigenspace is one-dimensional. Is A diagonalizable? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. No. The sum of the dimensions of the eigenspaces equals and the matrix has 3 columns. The sum of the dimensions of the eigenspace and the numb columns must be equal. OB. Yes. As long as the collection of eigenvectors spans R³, A is diagonalizable. OC. Yes. One of the eigenspaces would have OD. No. A matrix with 3 columns must have unique eigenvectors. Since the eigenvector for the third eigenvalue would also be unique, A must be diagona unique eigenvalues in order to be disonalizable
A is a 3x3 matrix with two eigenvalues. Each eigenspace is one-dimensional. Is A diagonalizable? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. No. The sum of the dimensions of the eigenspaces equals and the matrix has 3 columns. The sum of the dimensions of the eigenspace and the numb columns must be equal. OB. Yes. As long as the collection of eigenvectors spans R³, A is diagonalizable. OC. Yes. One of the eigenspaces would have OD. No. A matrix with 3 columns must have unique eigenvectors. Since the eigenvector for the third eigenvalue would also be unique, A must be diagona unique eigenvalues in order to be disonalizable
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A is a 3x3 matrix with two eigenvalues. Each eigenspace is one-dimensional. Is A diagonalizable? Why?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. No. The sum of the dimensions of the eigenspaces equals and the matrix has 3 columns. The sum of the dimensions of the eigenspace and the number of
columns must be equal.
OB. Yes. As long as the collection of eigenvectors spans R. A is diagonalizable.
OC. Yes. One of the eigenspaces would have
OD. No. A matrix with 3 columns must have
unique eigenvectors. Since the eigenvector for the third eigenvalue would also be unique, A must be diagonalizable
unique eigenvalues in order to be diagonalizable
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