Let A be an n x n matrix. Determine whether the statement below is true or false. Justify the answer.A matrix A is diagonalizable if A has n eigenvectors. Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer.A matrix A is diagonalizable if A has n eigenvectors.Choose the correct answer below.A. The statement is false. A diagonalizable matrix must have n linearly independent eigenvectors.B. The statement is false. A matrix is diagonalizable if and only if it has n-1 linearly independent eigenvectors.c. The statement is true. A diagonalizable matrix must have more than one linearly independent eigenvector.D. The statement is true. A diagonalizable matrix must have a minimum of n linearly independent eigenvectors.

As in the question we are given that the nxn matrix has n Eigen vectors we can find the solution to…

Answered: Let A be an nxn matrix. Determine…

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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Let A be an n x n matrix. Determine whether the statement below is true or false. Justify the answer.
A matrix A is diagonalizable if A has n eigenvectors.

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