
Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
5th Edition
ISBN: 9780134689531
Author: Lee Johnson, Dean Riess, Jimmy Arnold
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 4.7, Problem 1E
In Exercises 1 – 12, determine whether the given matrix A is diagonalizable. If A is diagonalizable, calculate
Expert Solution & Answer

Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Answer the questions
How can I prepare for me Unit 3 test in algebra 1? I am in 9th grade.
Solve the problem
Chapter 4 Solutions
Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...
Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - Using Eq.4, apply the singularity test to the...Ch. 4.1 - Using Eq.4, apply the singularity test to the...Ch. 4.1 - Using Eq.4, apply the singularity test to the...Ch. 4.1 - Using Eq.4, apply the singularity test to the...Ch. 4.1 - Consider the (22) symmetric matrix A=[abbd]. Show...Ch. 4.1 - Consider the (22) matrix A given by A=[abba],b0....Ch. 4.1 - Let A be a (22) matrix. Show that A and AT have...Ch. 4.2 - In Exercises 1-6, list the minor matrix Mij, and...Ch. 4.2 - In Exercises 1-6, list the minor matrix Mij, and...Ch. 4.2 - Prob. 3ECh. 4.2 - In Exercises 1-6, list the minor matrix Mij, and...Ch. 4.2 - Prob. 5ECh. 4.2 - In Exercises 1-6, list the minor matrix Mij, and...Ch. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - In Exercises 8-19, calculate the determinant of...Ch. 4.2 - Prob. 13ECh. 4.2 - In Exercises 8-19, calculate the determinant of...Ch. 4.2 - In Exercises 8-19, calculate the determinant of...Ch. 4.2 - In Exercises 8-19, calculate the determinant of...Ch. 4.2 - Prob. 17ECh. 4.2 - In Exercises 8-19, calculate the determinant of...Ch. 4.2 - Prob. 19ECh. 4.2 - Let A=(aij) be a given (33) matrix. Form the...Ch. 4.2 - In Exercises 21 and 22, find all ordered pairs...Ch. 4.2 - In Exercises 21 and 22, find all ordered pairs...Ch. 4.2 - Let A=(aij) be the (nn) matrix specified thus:...Ch. 4.2 - Let A and B be (nn) matrices. Use Theorems 2 and 3...Ch. 4.2 - Suppose that A is a (nn) nonsingular matrix, and...Ch. 4.2 - Prob. 26ECh. 4.2 - In Exercises 27-30, use Theorem 2 and Exercise 25...Ch. 4.2 - In Exercises 27-30, use Theorem 2 and Exercise 25...Ch. 4.2 - In Exercises 27-30, use Theorem 2 and Exercise 25...Ch. 4.2 - In Exercises 27-30, use Theorem 2 and Exercise 25...Ch. 4.2 - a Let A be an (nn) matrix. If n=3, det(A) can be...Ch. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.3 - In Exercise 1-6, evaluate det(A) by using row...Ch. 4.3 - In Exercise 1-6, evaluate det(A) by using row...Ch. 4.3 - Prob. 3ECh. 4.3 - In Exercise 1-6, evaluate det(A) by using row...Ch. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - In Exercise 7-12, use only column interchanges or...Ch. 4.3 - Prob. 9ECh. 4.3 - In Exercise 7-12, use only column interchanges or...Ch. 4.3 - In Exercise 7-12, use only column interchanges or...Ch. 4.3 - Prob. 12ECh. 4.3 - In Exercise 13-18, assume that the (33) matrix A...Ch. 4.3 - In Exercise 13-18, assume that the (33) matrix A...Ch. 4.3 - In Exercise 13-18, assume that the (33) matrix A...Ch. 4.3 - In Exercise 13-18, assume that the (33) matrix A...Ch. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - In Exercise 19-22, evaluate the (44) determinants....Ch. 4.3 - In Exercise 19-22, evaluate the (44) determinants....Ch. 4.3 - In Exercise 19-22, evaluate the (44) determinants....Ch. 4.3 - In Exercise 19-22, evaluate the (44) determinants....Ch. 4.3 - In Exercise 23 and 24, use row operations to...Ch. 4.3 - In Exercise 23 and 24, use row operations to...Ch. 4.3 - Let A be a (nn) matrix. Use Theorem 7 to argue...Ch. 4.3 - Prove the corollary to Theorem 6. Hint: Suppose...Ch. 4.3 - Find examples of (22) matrices A and B such that...Ch. 4.3 - An (nn) matrix A is called skew symmetric if AT=A....Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - Prove property b of theorem 11. Hint: Begin with...Ch. 4.4 - Prove property c of Theorem 11. Theorem 11 Let A...Ch. 4.4 - Complete the proof of property a of Theorem 11....Ch. 4.4 - Let qt=t3-2t2-t+2; and for any nn matrix H, define...Ch. 4.4 - With qt as in Exercise 18, verify that qC is the...Ch. 4.4 - Exercises 20 23 illustrate the Cayley-Hamilton...Ch. 4.4 - Exercises 20 23 illustrate the Cayley-Hamilton...Ch. 4.4 - Exercises 20 23 illustrate the Cayley-Hamilton...Ch. 4.4 - Exercises 20 23 illustrate the Cayley-Hamilton...Ch. 4.4 - This problem establishes a special case of the...Ch. 4.4 - Consider the 22 matrix A given by A=abcd. The...Ch. 4.4 - Prob. 26ECh. 4.4 - Let qt=tn+an-1tn-1++a1t+a0, and define the nn...Ch. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Prob. 34ECh. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - In Exercise 12-17, find the eigenvalues and the...Ch. 4.5 - In Exercise 12-17, find the eigenvalues and the...Ch. 4.5 - In Exercise 12-17, find the eigenvalues and the...Ch. 4.5 - In Exercise 12-17, find the eigenvalues and the...Ch. 4.5 - In Exercise 12-17, find the eigenvalues and the...Ch. 4.5 - In Exercise 12-17, find the eigenvalues and the...Ch. 4.5 - If a vector x is a linear combination of...Ch. 4.5 - As in Exercise 18, calculate A10x for...Ch. 4.5 - Consider a (44) matrix H of the form...Ch. 4.5 - An (nn) matrix P is called idempotent if P2=P....Ch. 4.5 - Let P be an idempotent matrix. Show that the only...Ch. 4.5 - Let u be a vector in Rn such that uTu=1. Show that...Ch. 4.5 - Verify that if Q is idempotent, then so is IQ....Ch. 4.5 - Suppose that u and v are vectors in Rn such that...Ch. 4.5 - Show that any nonzero vector of the form au+bv is...Ch. 4.5 - Prob. 27ECh. 4.5 - Let A be a symmetric matrix and suppose that Au=u,...Ch. 4.5 - Prob. 29ECh. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - Prob. 2ECh. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - Prob. 18ECh. 4.6 - Find the eigenvalues and the eigenvectors for the...Ch. 4.6 - Find the eigenvalues and the eigenvectors for the...Ch. 4.6 - Find the eigenvalues and the eigenvectors for the...Ch. 4.6 - Find the eigenvalues and the eigenvectors for the...Ch. 4.6 - Find the eigenvalues and the eigenvectors for the...Ch. 4.6 - Find the eigenvalues and the eigenvectors for the...Ch. 4.6 - In Exercises 25 and 26, solve the linear system....Ch. 4.6 - In Exercises 25 and 26, solve the linear system....Ch. 4.6 - In Exercises 27-30, calculate x. x=[1+i2]Ch. 4.6 - In Exercises 27-30, calculate x. x=[3+i2i]Ch. 4.6 - In Exercises 27-30, calculate x. x=[12ii3+i]Ch. 4.6 - In Exercises 27-30, calculate x. x=[2i1i3]Ch. 4.6 - Prob. 31ECh. 4.6 - In Exercises 31-34, use linear algebra software to...Ch. 4.6 - Prob. 33ECh. 4.6 - Prob. 34ECh. 4.6 - Establish the five properties of the conjugate...Ch. 4.6 - Let A be an (mn) matrix, and let B be an (np)...Ch. 4.6 - Prob. 37ECh. 4.6 - An (nn) matrix A is called Hermitian if A*=A....Ch. 4.6 - Let p(t)=a0+a1t+...+antn, where the coefficients...Ch. 4.6 - Prob. 40ECh. 4.6 - A real symmetric (nn) matrix A is called positive...Ch. 4.6 - An (nn) matrix A is called unitary if A*A=I. If A...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 13 18, use condition 5 to determine...Ch. 4.7 - In Exercises 13 18, use condition 5 to determine...Ch. 4.7 - In Exercises 13 18, use condition 5 to determine...Ch. 4.7 - In Exercises 13 18, use condition 5 to determine...Ch. 4.7 - In Exercises 13 18, use condition 5 to determine...Ch. 4.7 - In Exercises 13 18, use condition 5 to determine...Ch. 4.7 - In Exercises 19 and 20, find values ,,a,bandc such...Ch. 4.7 - In Exercises 19 and 20, find values ,,a,bandc such...Ch. 4.7 - Let A be an (nn) matrix, and let S be a...Ch. 4.7 - Show that if A is diagonalizable and if B is...Ch. 4.7 - Suppose that B is similar to A. Show each of the...Ch. 4.7 - Prove properties b and c of Theorem 21. Hint: For...Ch. 4.7 - Let u be a vector in Rn such that uTu=1. Let...Ch. 4.7 - Suppose that A and B are orthogonal (nn) matrices....Ch. 4.7 - Prob. 31ECh. 4.7 - Prob. 32ECh. 4.7 - Prob. 33ECh. 4.7 - Prob. 34ECh. 4.7 - Prob. 35ECh. 4.7 - Prob. 36ECh. 4.7 - Prob. 37ECh. 4.7 - Prob. 38ECh. 4.7 - Let B=QTAQ, where q and A are as in Exercise 38....Ch. 4.7 - Prob. 40ECh. 4.7 - Following the outline of Exercises 38-40, use...Ch. 4.7 - Consider the (nn) symmetric matrix A=(aij) defined...Ch. 4.7 - Suppose that A is a real symmetric matrix and that...Ch. 4.8 - In Exercises 1-6, consider the vector sequence...Ch. 4.8 - Prob. 2ECh. 4.8 - In Exercises 1-6, consider the vector sequence...Ch. 4.8 - Prob. 4ECh. 4.8 - In Exercises 1-6, consider the vector sequence...Ch. 4.8 - Prob. 6ECh. 4.8 - In Exercises 7-14, let xk=Axk1, k=1,2,....... for...Ch. 4.8 - Prob. 8ECh. 4.8 - In Exercises 7-14, let xk=Axk1, k=1,2,....... for...Ch. 4.8 - Prob. 10ECh. 4.8 - In Exercises 7-14, let xk=Axk1, k=1,2,, for the...Ch. 4.8 - Prob. 12ECh. 4.8 - Prob. 13ECh. 4.8 - Prob. 14ECh. 4.8 - Prob. 15ECh. 4.8 - In Exercises 15-18, solve the initial-value...Ch. 4.8 - Prob. 17ECh. 4.8 - Prob. 18ECh. 4.8 - Prob. 19ECh. 4.8 - Prob. 20ECh. 4.8 - Prob. 21ECh. 4.8 - Prob. 22ECh. 4.8 - Prob. 23ECh. 4.8 - Prob. 24ECh. 4.8 - Prob. 25ECh. 4.8 - Prob. 26ECh. 4.8 - Prob. 27ECh. 4.8 - Prob. 28ECh. 4.8 - Prob. 29ECh. 4.SE - Prob. 1SECh. 4.SE - Prob. 2SECh. 4.SE - Prob. 3SECh. 4.SE - Prob. 4SECh. 4.SE - Prob. 5SECh. 4.SE - Prob. 6SECh. 4.SE - Prob. 7SECh. 4.SE - Prob. 8SECh. 4.SE - Prob. 9SECh. 4.SE - Prob. 10SECh. 4.SE - Prob. 11SECh. 4.SE - Prob. 12SECh. 4.SE - Prob. 13SECh. 4.SE - Prob. 14SECh. 4.CE - CONCEPTUAL EXERCISES In Exercises 18, answer true...Ch. 4.CE - Prob. 2CECh. 4.CE - CONCEPTUAL EXERCISES In Exercises 18, answer true...Ch. 4.CE - Prob. 4CECh. 4.CE - Prob. 5CECh. 4.CE - Prob. 6CECh. 4.CE - Prob. 7CECh. 4.CE - CONCEPTUAL EXERCISES In Exercises 18, answer true...Ch. 4.CE - Prob. 9CECh. 4.CE - In Exercises 9-14, give a brief answer. Suppose...Ch. 4.CE - In Exercises 9-14, give a brief answer. Show that...Ch. 4.CE - In Exercises 9-14, give a brief answer. Let A and...Ch. 4.CE - Prob. 13CECh. 4.CE - In Exercises 9-14, give a brief answer. Let u be a...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- Solve the problemsarrow_forwardSolve the problems on the imagearrow_forwardAsked this question and got a wrong answer previously: Third, show that v3 = (−√3, −3, 3)⊤ is an eigenvector of M3 . Also here find the correspondingeigenvalue λ3 . Just from looking at M3 and its components, can you say something about the remaining twoeigenvalues? If so, what would you say?arrow_forward
- Determine whether the inverse of f(x)=x^4+2 is a function. Then, find the inverse.arrow_forwardThe 173 acellus.com StudentFunctions inter ooks 24-25/08 R Mastery Connect ac ?ClassiD-952638111# Introduction - Surface Area of Composite Figures 3 cm 3 cm 8 cm 8 cm Find the surface area of the composite figure. 2 SA = [?] cm² 7 cm REMEMBER! Exclude areas where complex shapes touch. 7 cm 12 cm 10 cm might ©2003-2025 International Academy of Science. All Rights Reserved. Enterarrow_forwardYou are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methodsarrow_forward
- Plane II is spanned by the vectors: - (2) · P² - (4) P1=2 P21 3 Subspace W is spanned by the vectors: 2 W1 - (9) · 1 W2 1 = (³)arrow_forwardshow that v3 = (−√3, −3, 3)⊤ is an eigenvector of M3 . Also here find the correspondingeigenvalue λ3 . Just from looking at M3 and its components, can you say something about the remaining twoeigenvalues? If so, what would you say? find v42 so that v4 = ( 2/5, v42, 1)⊤ is an eigenvector of M4 with corresp. eigenvalue λ4 = 45arrow_forwardChapter 4 Quiz 2 As always, show your work. 1) FindΘgivencscΘ=1.045. 2) Find Θ given sec Θ = 4.213. 3) Find Θ given cot Θ = 0.579. Solve the following three right triangles. B 21.0 34.6° ca 52.5 4)c 26° 5) A b 6) B 84.0 a 42° barrow_forward
- Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N then dim M = dim N but the converse need not to be true. B: Let A and B two balanced subsets of a linear space X, show that whether An B and AUB are balanced sets or nor. Q2: Answer only two A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}. fe B:Show that every two norms on finite dimension linear space are equivalent C: Let f be a linear function from a normed space X in to a normed space Y, show that continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence (f(x)) converge to (f(x)) in Y. Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as normed space B: Let A be a finite dimension subspace of a Banach space X, show that A is closed. C: Show that every finite dimension normed space is Banach space.arrow_forward• Plane II is spanned by the vectors: P12 P2 = 1 • Subspace W is spanned by the vectors: W₁ = -- () · 2 1 W2 = 0arrow_forwardThree streams - Stream A, Stream B, and Stream C - flow into a lake. The flow rates of these streams are not yet known and thus to be found. The combined water inflow from the streams is 300 m³/h. The rate of Stream A is three times the combined rates of Stream B and Stream C. The rate of Stream B is 50 m³/h less than half of the difference between the rates of Stream A and Stream C. Find the flow rates of the three streams by setting up an equation system Ax = b and solving it for x. Provide the values of A and b. Assuming that you get to an upper-triangular matrix U using an elimination matrix E such that U = E A, provide also the components of E.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage

Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Matrix Factorization - Numberphile; Author: Numberphile;https://www.youtube.com/watch?v=wTUSz-HSaBg;License: Standard YouTube License, CC-BY