Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.) Sufficient Condition for Diagonalization If an n x n matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable. Find the eigenvalues. (Enter your answers as a comma-separated list.) Is there a sufficient number to guarantee that the matrix is diagonalizable? O Yes O No

Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.) Sufficient Condition for Diagonalization If an n x n matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable. Find the eigenvalues. (Enter your answers as a comma-separated list.) Is there a sufficient number to guarantee that the matrix is diagonalizable? O Yes O No

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: Show that an n x n matrix A is invertible if and only if 0 is not an eigenvalue of A.

Q: A matrix of order n is diagonalizable if and only if A has n distinct eigenvalues. True False

A: To Find: If the statement is True or False: "A matrix of order n is diagonalizable if and only if A…

Q: Let A be an nxn matrix. Prove that if A is orthogonally diagonalizable (and has real eigenvalues),…

Q: Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee…

Q: Define a complex matrix B to be skew-Hermitian if Bh = −B. Show that if B is a complex matrix that…

A: We are given that B is a skew-harmattan matrix . And basically we have to show that 'every…

Q: Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee…

A: Let us consider matrix A; the eigenvalue of the matrix is obtained as: Determine the characteristic…

Q: Determine if the following statement is true or false, and explain why: If an n x n matrix is…

Q: Let A be an nxn diagonalizable matrix. Which one of the following is true Select one: a. Ther exists…

A: Given the matrix A is diagonalisable.

Q: Explain why the following statement is true or give a counterexample to show that it is false, as…

A: Two Eigen vector corresponding to same Eigen value are linearly dependent.

Q: Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee…

Q: Determine whether the following statement is True or False: Let A be an invertible triangular matrix…

A: Consider that eigenvalue of a triangular matrix are the diagonal elements of the matrix.

Q: Let A be an n × n matrix such that the sum of the elements from each row equals 1. Prove that A has…

A: Let's prove each statement separately:1. For a matrix A with row sums equal to 1: Let A be an n×n…

Q: The matrix A is a real symmetric 5 x 5 matrix with eigenvalues 3, 8, 12, 15, and 18. The vector x1…

A: Since

Q: 3 -1 Let B 7 -5 1 6. -6 2 Find all eigenvalues and a maximal set S of linearly independent…

A: Given: The matrix is B=3-117-516-62 To find the maximal set of the linearly independent eigenvector…

Q: The pedals of a bicycle are mounted on a bracket whose centre is 29.0 cm above the ground. Each…

A: Centre is 29 cm above the groundEach paddle is 17 cm from the bracketBicycle is padalled at 10…

Q: Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee…

A: We have the 2*2 square matrix A=1111we have to check if this is diagonalizable using it’s…

Question

2.
DETAILS
LARLINALG8 7.2.023.
MY NOTES
ASK YOUR TEACHER
Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may
be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.)
Sufficient Condition for Diagonalization
If an n x n matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable.
Find the eigenvalues. (Enter your answers as a comma-separated list.)
Is there a sufficient number to guarantee that the matrix is diagonalizable?
O Yes
O No

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let A be an eigenvalue of invertible matrix A. Prove that exists and is an eigenvalue of A-¹. What does your proof also say about the corresponding eigenvector?
The matrix A is a real symmetric 5 x 5 matrix with eigenvalues 3, 7, 10, 15, and 21. The vector xị is an eigenvector of A with eigenvalue 3, the vector x2 is an eigenvector of eigenvalue 10, the vector x4 is an eigenvector of A with eigenvalue 15, and the vector x; is an eigenvector of A with eigenvalue 21. with eigenvalue 7, the vector x3 is an eigenvector of A with Compute the dot products of the eigenvectors a; with each other. 21. x2 = I1. X3 = X1. 24 = x2 · X3 = I2 · X4 = X2 · X5 = 13 · X4 = 13 · X5 = X4: x5 =
Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.) Sufficient Condition for Diagonalization If an n x n matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable. 5 0 4 5 Find the eigenvalues. (Enter your answers as a comma-separated list.) Is there a sufficient number to guarantee that the matrix is diagonalizable? O Yes O No Need Help? Read It Submit Answer
Let A be an n x n matrix and let λ be an eigenvalue of A. The collection of all eigenvectors corresponding to A, together with the zero vector, is called the eigenspace of A and is denoted by EA. qs)Why is it important that this definition includes the phrase "together with the zero vector"? (i.e., what would go wrong if this phrase was not included?)
Prove that if A is a positive semidefinite matrix, then the singular valuesof A are the same as the eigenvalues of A.
If R is diagonalizable and Q is similar to R, then show that Q has n linearly independent eigenvectors. Also show that Q is invertible if R is invertible.
i. Show that the matrix is not diagonalizable. ii. Find the eigenvalues of the matrix and determine whether there is a sufficient number of eigenvalues to guarantee that the matrix is diagonalizable. -3 -2 3 3 4 -9 1. 2 -5)
Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.) Sufficient Condition for Diagonalization If an n x n matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable. [73] Find the eigenvalues. (Enter your answers as a comma-separated list.) λ =