A is a 3x3 matrix with two eigenvalues. Each eigenspace is one-dimensional. IsA diagonalizable? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Yes. One of the eigenspaces would have unique eigenvectors. Since the eigenvector for the third eigenvalue would also be unique, A must be diagonalizable. O B. Yes. As long as the collection of eigenvectors spans R°, A is diagonalizable. O C. 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. O D. No. A matrix with 3 columns must have unique eigenvalues in order to be diagonalizable.

A is a 3x3 matrix with two eigenvalues. Each eigenspace is one-dimensional. IsA diagonalizable? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Yes. One of the eigenspaces would have unique eigenvectors. Since the eigenvector for the third eigenvalue would also be unique, A must be diagonalizable. O B. Yes. As long as the collection of eigenvectors spans R°, A is diagonalizable. O C. 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. O D. No. A matrix with 3 columns must have unique eigenvalues in order to be diagonalizable.

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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Question

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.
A. Yes. One of the eigenspaces would have
unique eigenvectors. Since the eigenvector for the third eigenvalue would also be unique, A must be diagonalizable.
O B. Yes. As long as the collection of eigenvectors spans R°, A is diagonalizable.
C. 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.
D. No. A matrix with 3 columns must have
unique eigenvalues in order to be diagonalizable.

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