T F Matrices with the same eigen values must be similar T F Similar matrices must...

Question

Question

T F Matrices with the same eigen values must be similar

T F Similar matrices must have the same eigen vectors

T F Similar matrices must have the same eigen values

T F Similar matrices must have the same characteristic polynomial

T F If A and B are similar, then they must be invertible

T F If A and B are similar and are both invertible, then A^(-1) is similar to B^(-1)

Answer 1

Answer #1

③ Matrices with same Similar True. eigen.values must be Talse Take 3 ③ Similar matrices must have same eigenvector, A- [ ] ri

Answer 2

Similar Homework Help Questions

Find the eigen values and eigen vectors of the following matrices: Give each step Answers without...

Find the eigen values and eigen vectors of the following matrices: Give each step Answers without intermediate steps will not be accepted.
Let А and B be similar nxn matrices. That is, we can write A = CBC-...

Let А and B be similar nxn matrices. That is, we can write A = CBC- for some invertible matrix с Then the matrices A and B have the same eigenvalues for the following reason(s). A. Both А and A. Both А and B have the same characteristic polynomial. B. Since A = CBC-1 , this implies A = CC-B = IB = B and the matrices are equal. C. Suppose that 2 is an eigenvalue for the matrix B...
let a and b be n*n similar matrices, namely, B=S^-1 AS. show that the matrices a...

let a and b be n*n similar matrices, namely, B=S^-1 AS. show that the matrices a and b have the same characteristic polynomial, det(a-λI)=det(b-λI) and, consequently, the same eigenvalues.

Two n x n matrices A and B are called similar if there is an invertible...

Two n x n matrices A and B are called similar if there is an invertible matrix P such that B = P-AP. Show that two similar matrices enjoy the following properties. (a) They have the same determinant. (b) They have the same eigenvalues: specifically, show that if v is an eigenvector of A with eigenvalue 1, then P-lv is an eigenvector of B with eigenvalue l. (c) For any polynomial p(x), P(A) = 0 is equivalent to p(B) =...
Problem 5. Let n N. The goal of this problem is to show that if two real n x n matrices are simil...

Problem 5. Let n N. The goal of this problem is to show that if two real n x n matrices are similar over C, then they are also similar over IK (a) Prove that for all X, y є Rnxn, the function f(t) det (X + ty) is a polynomial in t. (b) Prove that if X and Y are real n × n matrices such that X + ừ is an invertible complex matrix, then there exists a...
8: Suppose that A and B are similar matrices, B = p-1AP, where 6 2 P...

8: Suppose that A and B are similar matrices, B = p-1AP, where 6 2 P = -1 1 We know that A and B have the same characteristic polynomial and the same eigenvalues. Suppose that 2 is one of the common eigenvalues and x = [4 1] is a corresponding eigenvector of A. Which of the following is the eigenvector of B corresponding to 2 ? "f1-4-0-0-0-0-01-10 #8: Select

19. Suppose A and B are n xn matrices. a. Suppose that both A and B...

19. Suppose A and B are n xn matrices. a. Suppose that both A and B are diagonalizable and that they have the same eigen- vectors. Prove that AB = BA. b. Suppose A has n distinct eigenvalues and AB = BA. Prove that every eigen vector of A is also an eigen vector of B. Conclude that B is diagonalizable. (Query: Need every eigenvector of B be an eigenvector of A?)
oru 2 Let A and B be two n x n matrices. There exists a nonsingular...

oru 2 Let A and B be two n x n matrices. There exists a nonsingular matrix P such that PB = AP. Then which of the following is always true? a) A and B are not similar b) A and B have the same eigenvalues c) A does not have any characteristic polynomial d) B does not have any characteristic polynomial
We say that A and B are similar matrices if A = SBS-1 for some invertible...

We say that A and B are similar matrices if A = SBS-1 for some invertible matrix S. Are the following true or false. Given a mathematical reason (proof). (a) If A and B are similar, then A and B have the same eigenvalues. Answer: (b) If A and B are similar, then A and B have the same eigenvectors. Answer: c) If A and B are similar, then A - 51 and B – 51 are similar. Answer: (d)...

Exercise 1.6 Give all possible Jordan canonical forms of matrices that have characteristic poly- nomial (t...

Exercise 1.6 Give all possible Jordan canonical forms of matrices that have characteristic poly- nomial (t + π)4(1-2)3(t + 2i) and minimal polynomial (t + π)2(t-2)(t + 2). Exercise 1.7 Let A = | 0 1-3) , B = | 2 1 -W | . Are A and B similar? 0 0 1