(1) True or False? Justify your answer. (a) There exists a matrix A with eigenvalue 4 whose algebraic multiplicity is 1 and geo- metric multiplicity is 3. Justification: (b) Matrix 3 4 Justification: True Justification: in Z5 is digonalizable. True False (c) Two matrices A and B are similar if they have the same list of eigenvalues that have the same algebraic multiplicity. True False False

(1) True or False? Justify your answer. (a) There exists a matrix A with eigenvalue 4 whose algebraic multiplicity is 1 and geo- metric multiplicity is 3. Justification: (b) Matrix 3 4 Justification: True Justification: in Z5 is digonalizable. True False (c) Two matrices A and B are similar if they have the same list of eigenvalues that have the same algebraic multiplicity. True False False

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: Find eigenvalue, and eizenvectors of the matrix - 14 12 1 - 20 17

A: The given matrix is -1412-2017 We have to find the eigenvalues and corresponding eigenvectors of…

Q: Prove that if A is a symmetric orthogonal matrix, then 1 and -1 are the only possible eigenvalues.

Q: -3 -1 -3 11. Given the matrix W = 3 -2 -1 -2 (a) Find all the eigenvalues of W (b) Find all eigen…

A: According to question, Given matrix, W = -3-1-3030-2-1-2

Q: 1. Mark as TRUE or FALSE. If they are true give an explanation, if they are false, give a coun-…

A: NOTE: Since we can solve at most one problem at a time we have solved the first question. Kindly…

Q: To prepare for your discussion activity, find an article or other resource about the application of…

A: find an article or other resource about the application of linear algebra concepts in the real…

Q: 1) Explain why 2 x 2 rotation matrices cannot be diagonalized (using real matrices). Your answer…

Q: (5) Prove that if A is a square matrix, then A and AT have the same eigenvalues. Bonus ques- tion:…

Q: (IV) There exists a matrix A with eigenvalue 5 whose algebraic multiplicity is 2 and geo- metric…

A: We have to find if the statement is true or false.

Q: what you know about the eigenvalues, trace, and determinant of A

A: The answer is given as

Q: 3 -1 Let A be the 2 x 2 matrix 1 Q5. 1 (a) Find an eigenbasis B for A. (b) Find the B-matrix for A.…

Q: Suppose that S is an orthogonal and symmetric matrix. What are all possible eigenvalues of S?…

Q: (i) There exists a matrix that is diagonalizable but not invertible. (j) If A is an eigenvalue of…

Q: 19. As in Exercise 18, calculate A¹0x for 1 2-1 05-2 6-2 A = 0 and x = 2 4]. 7

Q: Is the quadratic form A = 1 positive definite, negative definite, positive semi-definite, negative…

Q: -1 3 -12 0 5 -2 -1 ^- |- Determine whether A is diagonalizable. late (4)10 If A is diagonalizable,…

Q: 1 Mark as TRUE or FALSE. If they are true give an explanation, if they are false, give a coun-…

Q: True or False? Upload your reasoning. If the statement is true give a proof or detailed reason why…

Question

(1)
True or False? Justify your answer.
(a) There exists a matrix A with eigenvalue 4 whose algebraic multiplicity is 1 and geo-
metric multiplicity is 3.
Justification:
(b) Matrix
[13]
Justification:
True
in Z5 is digonalizable.
True
Justification:
(c) Two matrices A and B are similar if they have the same list of eigenvalues that have
the same algebraic multiplicity.
False
Justification:
True
False
False
(d) A square matrix with the characteristic polynomial A5 - 314-2A³ +5A² - 4x + 2 is
invertible.
True
False
(e) If A and B are similar then both of them are diagonalizable.
True
False
Justification:

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduce rules of Bartleby

VIEW

Step 2: Explain part a, b

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

Can you solve part D and E as well.

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

Describe all least-squares solutions of the equation Ax = b. 重 110 1 110 b 10 1 A = 101 12 The general least-squares solutions of Ax = b for the given matrix A and vector b are all vectors of the form x =+x (Simplify your answers.) with x, free.
True/False along with reasons and explanations- A is an nxn matrix that has no inverse, so the only eigenvalues of A is 0.- If the vector v is an eigenvector of the matrix A, then kv is also an eigenvector provided that k ≠ 0.- A is row equivalent to B, then A and B have the same eigenvalues.- It is known that the two eigenvectors are linearly independent, it can be concluded that they come from different eigenspaces.- Every matrix that has an inverse can be diagonalized.- If A is a non-singular matrix that can be diagonalized, then A^T and A^-1 can also be diagonalized.- A matrix of order 3x3. There is a basis R^3 which consists of the eigenvectors of A. Then A can be diagonalized.- If the matrix can be diagonalized, then the matrix is diagonally single.- A and B are similar to each other. B and C are similar, so det(A) = det(C)
State whet her each statement is true or false and provide a short justification for your claim (a short proof if you think the statement is true or a counter example if you think it is false). (a) Let Apxn, n > 1, be a matrix such that RREF(A) has only one pivot column. Let i be a nonzero vector in Col(A). Then is an eigenvector for A. (b) Let T :V → W be a linear transformation, and suppose that w e V is a linear combination of the vectors õ1, ..., Un in V. Then T(w) is a linear combination of the vectors T(71),...,T(ūn).
Matrix A is factored in the form PDP - 1 Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 3 0 2 -1 0 - 1 5 0 0 1 - A = 6 5 6. 1 3 050 3 1 3 0 0 1 0 0 3 -1 0 - 1 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) O A. There is one distinct eigenvalue, A =. A basis for the corresponding eigenspace is { }. B. In ascending order, the two distinct eigenvalues are , = and 12 = Bases for the corresponding eigenspaces are { and { , respectively. %3D C. In ascending order, the three distinct eigenvalues are , =, 12 = and A3 = Bases for the corresponding eigenspaces are {0{}, and {}, respectively.
True or False? Justify your answer. Answers without correct justification will receive no credit. e) If A and B are similar then both of them are diagonalizable. □ True □ False c) Two matrices A and B are similar if they have the same list of eigenvalues that have the same algebraic multiplicity.□ True □ False a)
Linear Algebra . What is the definition of an eigenvector and an eigenvalue of a square matrix A?
1 3 is diagonalizable. Its eigenvectors are: 4 2 The matrix A = 3. 2 4 3 4