Note :
A.M.= repetition of an eigen value
G.M.= no. Of L.I. eigen vector for given eigen value
6) Let A be a 5x5 matrix, with 3 different eigenvalues, and let a be an...
6) Let A be a 5x5 matrix, with 3 different eigenvalues, and let 2 be an eigenvalue of multiplicity 3. If A-2/ has rank 2, is A defective? (Explain, as a yes or no answer will receive no credit).
6) Let A be a 5x5 matrix, with 3 different eigenvalues, and let i be an eigenvalue of multiplicity 3. If A-11 has rank 2, is A defective? (Explain, as a yes or no answer will receive no credit).
(1 point) Suppose a 3 x 3 matrix A has only two distinct eigenvalues. Suppose that tr(A) = 1 and det(A) = 63. Find the eigenvalues of A with their algebraic multiplicities. The smaller eigenvalue has multiplicity and the larger eigenvalue has multiplicity
9. Let Q1 S Q2 be the eigenvalues of the matrix A and Qs 1 if Qi is a defective eigenvalue and Q. - 0 otherwise, where 86 100 01-81-94 T < 1 Let Q = 1013 + IQ1 + 2(Qal + 3(Qal). Then T = 5 sin2(100Q) satisfies:-(A) 0 (B) 1 T < 2.
9. Let Q1 S Q2 be the eigenvalues of the matrix A and Qs 1 if Qi is a defective eigenvalue and Q. - 0...
(b) The matrix B= 1 2 2 3 3 1 3 2 4 has eigenvalues 7,2, -1. i. Find a column and a row eigenvector of B corresponding to the Perron eigenvalue. ii. Find a rank one nonnegative matrix C such that the matrix B+C will have eigenvalues 13, 2, -1. iii. Let a and B be real numbers. Calculate the eigenvalues of D(a, b) = aB+ BC. iv. Find limno(+B)"
Question 21 Let T:R+ R2 be the transformation of rotation counterclockwise by 30 degrees, and let A be the standard matrix for T. Which one of the following statements must be true about A? A has one real eigenvalue with algebraic multiplicity 2. A has two distinct real eigenvalues. A has one real eigenvalue and one complex eigenvalue. A has two distinct complex eigenvalues. Question 22 Suppose A is a positive stochastic 2 x 2 matrix and A As n...
estion 3 Let A be an n x n symmetric matrix. Then, which of the following is not true? a) A is diagonalizable. b) If I is an eigenvalue of A with multiplicity k, then the eigenspace of has dimension k c) Some eigenvalues of A can be complex. d) All eigenvalues of A are real.
3 1. Let A = 0 (a) Compute the eigenvalues of A and specify their algebraic multiplicities. (b) For every eigenvalue 1, determine the eigenspace Ex and specify its dimension. (c) Is A a defective matrix? Why or why not? (d) Is A a singular matrix? Why or why not? (e) Determine the eigenvalues of (74) + 5.
6 8. Let A be a square matrix one of whose eigenvalues are 1. Is 12 an eigenvalue of B2. Why or why not?
hi, can you write the notation
and everything?
Assignment 12 Let A= -3 -5 -2 6 8 2 0 0 -2 [3pt] (a) Find the eigenvalues of A. (1pt] (b) Determine the algebraic multiplicity of each eigenvalue of A. [3pt] (c) Find a basis for each eigenspace for A. (1pt] (d) Determine the geometric multiplicity of each eigenvalue of A. [2pt] (e) Give a matrix P and a diagonal matrix D such that P-1AP = D.