Let A be an nn matrix. Determine whether the statement below is true or false. Justify the answer.If A is diagonalizable, then A has n distinct eigenvalues. Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer.If A is diagonalizable, then A has n distinct eigenvalues.Choose the correct answer below.O A. The statement is false. A diagonalizable matrix must have more than n eigenvalues.B. The statement is true. A diagonalizable matrix must have exactly n eigenvalues.c. The statement is false. A diagonalizable matrix can have fewer than n eigenvalues and still have n linearly independent eigenvectors.D. The statement is true. A diagonalizable matrix must have n distinct eigenvalues.

Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer. If A is diagonalizable, then A has n distinct eigenvalues. Choose the correct answer below. A. The statement is false. A diagonalizable matrix must have more than n eigenvalues. B. The statement is true. A diagonalizable matrix must have exactly n eigenvalues. c. The statement is false. A diagonalizable matrix can have fewer than n eigenvalues and still have n linearly independent eigenvectors. O D. The statement is true. A diagonalizable matrix must have n distinct eigenvalues.

Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer. If A is diagonalizable, then A has n distinct eigenvalues. Choose the correct answer below. A. The statement is false. A diagonalizable matrix must have more than n eigenvalues. B. The statement is true. A diagonalizable matrix must have exactly n eigenvalues. c. The statement is false. A diagonalizable matrix can have fewer than n eigenvalues and still have n linearly independent eigenvectors. O D. The statement is true. A diagonalizable matrix must have n distinct eigenvalues.

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

Let A be an nn matrix. Determine whether the statement below is true or false. Justify the answer.
If A is diagonalizable, then A has n distinct eigenvalues.

Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer.
If A is diagonalizable, then A has n distinct eigenvalues.
Choose the correct answer below.
O A. The statement is false. A diagonalizable matrix must have more than n eigenvalues.
B. The statement is true. A diagonalizable matrix must have exactly n eigenvalues.
c. The statement is false. A diagonalizable matrix can have fewer than n eigenvalues and still have n linearly independent eigenvectors.
D. The statement is true. A diagonalizable matrix must have n distinct eigenvalues.

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