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Is the matrix b) Suppose A = 0 is an eigenvalue of a matrix. Is the vector 0 a possible candidate for the corresponding eigenvector? c) Let A be a non-symmetric square matrix. Which of the following three matrices are non- symetric? 1. AAT 2. 3. AT. A + AT [] diagonalizable? d) which of these are orthogonal matrices? Select one: O a. [1/√2 -√2/6 2/3 1/√√/2 √2/6 -2/3 0 2√2/3 1/3] O b. [1-2/6 2/3] 1 2/6 -2/3 4/3 1/3] 0 c. [1/√/2 0 2/31 1/√2-1/√2-2/3 0 1/√/2 1/3 O d. There are no orthogonal matrices here!

Is the matrix b) Suppose A = 0 is an eigenvalue of a matrix. Is the vector 0 a possible candidate for the corresponding eigenvector? c) Let A be a non-symmetric square matrix. Which of the following three matrices are non- symetric? 1. AAT 2. 3. AT. A + AT [] diagonalizable? d) which of these are orthogonal matrices? Select one: O a. [1/√2 -√2/6 2/3 1/√√/2 √2/6 -2/3 0 2√2/3 1/3] O b. [1-2/6 2/3] 1 2/6 -2/3 4/3 1/3] 0 c. [1/√/2 0 2/31 1/√2-1/√2-2/3 0 1/√/2 1/3 O d. There are no orthogonal matrices here!

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 37EQ
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a) Is the matrix b) [10] Suppose X = 0 is an eigenvalue of a matrix. Is the vector 0 a possible candidate for the corresponding eigenvector? diagonalizable? c) Let A be a non-symmetric square matrix. Which of the following three matrices are non- symetric? 1. AAT 2. A+ AT 3. AT O b. d) Which of these are orthogonal matrices? Select one: O a. [1/√2 -√2/6 2/31 1/√/2 √2/6 -2/3 0 2√/2/3 1/3] 1 -2/6 2/31 1 2/6 -2/3 0 4/3 1/3] 0 O c. [1/√2 2/3] 1/√2 -1/√2 -2/3 0 1/√/2 1/3 O d. There are no orthogonal matrices here! e) A symmetric matrix has two distinct eigenvalues. The first eigenvalue has B as a corresponding eigenvector. Which one of the following vectors could be an eigenvector for the other eigenvalue? Select one: O a. a O b. Oc B H Od. [1/√14] 2/√/14 [3/√14] Let A - and P -B3 Solve the following system of linear differential equations. У1 - буı - Зуг ½/₂2 73/2-271 [2] -2 - - [69] 09 Then P is an invertible matrix satisfying P-AP- Activate Wind Go to Settings to a
Transcribed Image Text:a) Is the matrix b) [10] Suppose X = 0 is an eigenvalue of a matrix. Is the vector 0 a possible candidate for the corresponding eigenvector? diagonalizable? c) Let A be a non-symmetric square matrix. Which of the following three matrices are non- symetric? 1. AAT 2. A+ AT 3. AT O b. d) Which of these are orthogonal matrices? Select one: O a. [1/√2 -√2/6 2/31 1/√/2 √2/6 -2/3 0 2√/2/3 1/3] 1 -2/6 2/31 1 2/6 -2/3 0 4/3 1/3] 0 O c. [1/√2 2/3] 1/√2 -1/√2 -2/3 0 1/√/2 1/3 O d. There are no orthogonal matrices here! e) A symmetric matrix has two distinct eigenvalues. The first eigenvalue has B as a corresponding eigenvector. Which one of the following vectors could be an eigenvector for the other eigenvalue? Select one: O a. a O b. Oc B H Od. [1/√14] 2/√/14 [3/√14] Let A - and P -B3 Solve the following system of linear differential equations. У1 - буı - Зуг ½/₂2 73/2-271 [2] -2 - - [69] 09 Then P is an invertible matrix satisfying P-AP- Activate Wind Go to Settings to a
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