EBK LINEAR ALGEBRA AND ITS APPLICATIONS
EBK LINEAR ALGEBRA AND ITS APPLICATIONS
6th Edition
ISBN: 9780135851043
Author: Lay
Publisher: PEARSON CO
bartleby

Videos

Textbook Question
Book Icon
Chapter 5.7, Problem 1PP

A real 3 × 3 matrix A has eigenvalues −.5, .2 + .3i, and .2 − .3i, with corresponding eigenvectors

v1 = [ 1 − 2 1 ] , v2= [ 1 + 2 i 4 i 2 ] , and v3 = [ 1 − 2 i − 4 i 2 ]

1. Is A diagonalizable as A = PDP−1, using complex matrices?

Expert Solution & Answer
Check Mark
bartleby

Learn your wayIncludes step-by-step video

See solution
Check out sample textbook solution
Blurred answer
03:19
Previous
Chapter 5.6, Problem 18E
Next
Chapter 5.7, Problem 2PP

Chapter 5 Solutions

EBK LINEAR ALGEBRA AND ITS APPLICATIONS

Ch. 5.1 - Is 5 an eigenvalue of A=[631305226]?Ch. 5.1 - If x is an eigenvector of A corresponding to ,...Ch. 5.1 - Suppose that b1 and b2 are eigenvectors...Ch. 5.1 - If A is an n n matrix and is an eigenvalue of A,...Ch. 5.1 - Is = 2 an eigenvalue of [3238]? Why or why not?Ch. 5.1 - Is = 2 an eigenvalue of [7331]? Why or why not?Ch. 5.1 - Is [14] an eigenvalue of [3138]? If so, find the...Ch. 5.1 - Is [431] an eigenvalue of [379451244]? If so, find...Ch. 5.1 - Prob. 6ECh. 5.1 - Is = 4 an eigenvalue of [301231345]? If so, find...
Ch. 5.1 - Is = 3 an eigenvalue of [122321011]? If so, find...Ch. 5.1 - In Exercises 9-16, find a basis for the eigenspace...Ch. 5.1 - In Exercises 9-16, find a basis for the eigenspace...Ch. 5.1 - In Exercises 9-16, find a basis for the eigenspace...Ch. 5.1 - Prob. 12ECh. 5.1 - In Exercises 9-16, find a basis for the eigenspace...Ch. 5.1 - In Exercises 9-16, find a basis for the eigenspace...Ch. 5.1 - In Exercises 9-16, find a basis for the eigenspace...Ch. 5.1 - Find the eigenvalues of the matrices in Exercises...Ch. 5.1 - Find the eigenvalues of the matrices in Exercises...Ch. 5.1 - For A=[123123123], find one eigenvalue, with no...Ch. 5.1 - In Exercises 21—30, A is an nn matrix. Mark each...Ch. 5.1 - In Exercises 21—30, A is an nn matrix. Mark each...Ch. 5.1 - In Exercises 21—30, A is an nn matrix. Mark each...Ch. 5.1 - In Exercises 21—30, A is an nn matrix. Mark each...Ch. 5.1 - Prob. 25ECh. 5.1 - In Exercises 21—30, A is an nn matrix. Mark each...Ch. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Explain why a 2 2 matrix can have at most two...Ch. 5.1 - Construct an example of a 2 2 matrix with only...Ch. 5.1 - Let be an eigenvalue of an invertible matrix A....Ch. 5.1 - Show that if A2 is the zero matrix, then the only...Ch. 5.1 - Show that is an eigenvalue of A if and only if ...Ch. 5.1 - Consider an n n matrix A with the property that...Ch. 5.1 - In Exercises 31 and 32, let A be the matrix of the...Ch. 5.1 - T is the transformation on 3 that rotates points...Ch. 5.1 - Let u and v be eigenvectors of a matrix A, with...Ch. 5.1 - Describe how you might try to build a solution of...Ch. 5.1 - Let u and v be the vectors shown in the figure,...Ch. 5.2 - Find the characteristic equation and eigenvalues...Ch. 5.2 - Find the characteristic polynomial and the...Ch. 5.2 - Find the characteristic polynomial and the...Ch. 5.2 - Find the characteristic polynomial and the...Ch. 5.2 - Find the characteristic polynomial and the...Ch. 5.2 - Find the characteristic polynomial and the...Ch. 5.2 - Prob. 6ECh. 5.2 - Find the characteristic polynomial and the...Ch. 5.2 - Find the characteristic polynomial and the...Ch. 5.2 - Exercises 914 require techniques from Section 3.1....Ch. 5.2 - Exercises 914 require techniques from Section 3.1....Ch. 5.2 - Exercises 914 require techniques from Section 3.1....Ch. 5.2 - Exercises 9—14 require techniques from Section...Ch. 5.2 - Exercises 914 require techniques from Section 3.1....Ch. 5.2 - Prob. 14ECh. 5.2 - For the matrices in Exercises 1517, list the...Ch. 5.2 - For the matrices in Exercises 15-17, list the...Ch. 5.2 - For the matrices in Exercises 15-17, list the...Ch. 5.2 - It can be shown that the algebraic multiplicity of...Ch. 5.2 - Let A be an n n matrix, and suppose A has n real...Ch. 5.2 - Use a property of determinants to show that A and...Ch. 5.2 - In Exercises 21—30, A and B are nn matrices....Ch. 5.2 - In Exercises 21—30, A and B are nn matrices....Ch. 5.2 - In Exercises 21—30, A and B are nn matrices....Ch. 5.2 - Prob. 25ECh. 5.2 - A widely used method for estimating eigenvalues of...Ch. 5.2 - Show that if A and B are similar, then det A = det...Ch. 5.3 - Compute A8, where A = [4321].Ch. 5.3 - Let A = [31227], v1 = [31], and v2 = [21]. Suppose...Ch. 5.3 - Let A be a 4 4 matrix with eigenvalues 5, 3, and...Ch. 5.3 - In Exercises 1 and 2, let A = PDP1 and compute A4....Ch. 5.3 - In Exercises 1 and 2, let A = PDP1 and compute A4....Ch. 5.3 - In Exercises 3 and 4, use the factorization A =...Ch. 5.3 - Prob. 4ECh. 5.3 - In Exercises 5 and 6. the matrix A is factored in...Ch. 5.3 - Diagonalize the matrices in Exercises 720, if...Ch. 5.3 - Diagonalize the matrices in Exercises 720, if...Ch. 5.3 - Diagonalize the matrices in Exercises 720, if...Ch. 5.3 - Diagonalize the matrices in Exercises 720, if...Ch. 5.3 - Diagonalize the matrices in Exercises 720, if...Ch. 5.3 - Diagonalize the matrices in Exercises 720, if...Ch. 5.3 - Diagonalize the matrices in Exercises 720, if...Ch. 5.3 - Diagonalize the matrices in Exercises 720, if...Ch. 5.3 - Diagonalize the matrices in Exercises 720, if...Ch. 5.3 - Diagonalize the matrices in Exercises 720, if...Ch. 5.3 - Diagonalize the matrices in Exercises 720, if...Ch. 5.3 - A is a 5 5 matrix with two eigenvalues. One...Ch. 5.3 - A is a 3 3 matrix with two eigenvalues. Each...Ch. 5.3 - A is a 4 4 matrix with three eigenvalues. One...Ch. 5.3 - A is a 7 7 matrix with three eigenvalues. One...Ch. 5.3 - Show that if A is both diagonalizable and...Ch. 5.3 - Show that if A has n linearly independent...Ch. 5.3 - A factorization A = PDP1 is not unique....Ch. 5.3 - With A and D as in Example 2, find an invertible...Ch. 5.3 - Construct a nonzero 2 2 matrix that is invertible...Ch. 5.3 - Construct a nondiagonal 2 2 matrix that is...Ch. 5.4 - Find T(a0 + a1t + a1t2), if T is the linear...Ch. 5.4 - Let A, B, and C be n n matrices. The text has...Ch. 5.4 - Let B = b1,b2,b3 and D = d1,d2 be bases for vector...Ch. 5.4 - Assume the mapping T : 2 2 defined by T(a0 + a1t...Ch. 5.4 - Prob. 4ECh. 5.4 - Let B = {b1, b2, b3} be a basis for a vector space...Ch. 5.4 - In Exercises 11 and 12, find the B-matrix for the...Ch. 5.4 - In Exercises 11 and 12, find the B-matrix for the...Ch. 5.4 - In Exercises 1316, define T : 2 2 by T(x) = Ax....Ch. 5.4 - In Exercises 1316, define T : 2 2 by T(x) = Ax....Ch. 5.4 - In Exercises 1316, define T : 2 2 by T(x) = Ax....Ch. 5.4 - In Exercises 1316, define T : 2 2 by T(x) = Ax....Ch. 5.4 - Let A = [1113] and B = {b1, b2}, for b1 = [11], b2...Ch. 5.4 - Define T : 3 3 by T (x) = Ax, where A is a 3 3...Ch. 5.5 - Show that if a and b are real, then the...Ch. 5.5 - Let each matrix in Exercises 16 act on 2. Find the...Ch. 5.5 - Let each matrix in Exercises 16 act on 2. Find the...Ch. 5.5 - Let each matrix in Exercises 16 act on 2. Find the...Ch. 5.5 - Let each matrix in Exercises 16 act on 2. Find the...Ch. 5.5 - In Exercises 712, use Example 6 to list the...Ch. 5.5 - In Exercises 712, use Example 6 to list the...Ch. 5.5 - In Exercises 712, use Example 6 to list the...Ch. 5.5 - In Exercises 712, use Example 6 to list the...Ch. 5.5 - In Exercises 1320, find an invertible matrix P and...Ch. 5.5 - In Exercises 1320, find an invertible matrix P and...Ch. 5.5 - In Exercises 1320, find an invertible matrix P and...Ch. 5.5 - In Exercises 1320, find an invertible matrix P and...Ch. 5.5 - In Example 2, solve the first equation in (2) for...Ch. 5.5 - Let A be a complex (or real) n n matrix, and let...Ch. 5.5 - Let A be a real n n matrix, and let x be a vector...Ch. 5.5 - Let A be a real 2 2 matrix with a complex...Ch. 5.6 - The matrix A below has eigenvalues 1, 23, and 13,...Ch. 5.6 - What happens to the sequence {xk } in Practice...Ch. 5.6 - Let A be a 2 2 matrix with eigenvalues 3 and 1/3...Ch. 5.6 - Suppose the eigenvalues of a 3 3 matrix A are 3,...Ch. 5.6 - In Exercises 36, assume that any initial vector x0...Ch. 5.6 - Determine the evolution of the dynamical system in...Ch. 5.6 - In old-growth forests of Douglas fir, the spotted...Ch. 5.6 - Show that if the predation parameter p in Exercise...Ch. 5.6 - Let A have the properties described in Exercise 1....Ch. 5.6 - Prob. 8ECh. 5.6 - In Exercises 914, classify the origin as an...Ch. 5.6 - In Exercises 914, classify the origin as an...Ch. 5.6 - In Exercises 914, classify the origin as an...Ch. 5.6 - In Exercises 914, classify the origin as an...Ch. 5.6 - In Exercises 914, classify the origin as an...Ch. 5.6 - In Exercises 914, classify the origin as an...Ch. 5.6 - Let A = [.40.2.3.8.3.3.2.5]. The vector v1 = [163]...Ch. 5.7 - A real 3 3 matrix A has eigenvalues .5, .2 + .3i,...Ch. 5.7 - A real 3 3 matrix A has eigenvalues .5, .2 + .3i....Ch. 5.7 - A real 3 3 matrix A has eigenvalues 5, .2 + .3i,...Ch. 5.7 - A panicle moving in a planar force field has a...Ch. 5.7 - Let A be a 2 2 matrix with eigenvalues 3 and 1...Ch. 5.7 - In Exercises 36, solve the initial value problem...Ch. 5.7 - In Exercises 36, solve the initial value problem...Ch. 5.7 - In Exercises 36, solve the initial value problem...Ch. 5.7 - In Exercises 36, solve the initial value problem...Ch. 5.7 - In Exercises 7 and 8, make a change of variable...Ch. 5.7 - In Exercises 7 and 8, make a change of variable...Ch. 5.7 - In Exercises 918, construct the general solution...Ch. 5.7 - In Exercises 918, construct the general solution...Ch. 5.7 - In Exercises 918, construct the general solution...Ch. 5.7 - In Exercises 918, construct the general solution...Ch. 5.7 - In Exercises 918, construct the general solution...Ch. 5.7 - In Exercises 918, construct the general solution...Ch. 5.7 - [M] Find formulas for the voltages v1 and v2 (as...Ch. 5.7 - [M] Find formulas for the voltages v1 and v2 for...Ch. 5.7 - [M] Find formulas for the current it and the...Ch. 5.7 - [M] The circuit in the figure is described by the...Ch. 5.8 - How can you tell if a given vector x is a good...Ch. 5.8 - In Exercises 14, the matrix A is followed by a...Ch. 5.8 - In Exercises 14, the matrix A is followed by a...Ch. 5.8 - In Exercises 14, the matrix A is followed by a...Ch. 5.8 - In Exercises 14, the matrix A is followed by a...Ch. 5.8 - Let A = [15162021]. The vectors x, , A5x are...Ch. 5.8 - Let A = [2367]. Repeat Exercise 5, using the...Ch. 5.8 - Exercises 13 and 14 apply to a 3 3 matrix A whose...Ch. 5.8 - Exercises 13 and 14 apply to a 3 3 matrix A whose...Ch. 5.8 - Suppose Ax = x with x 0. Let or be a scalar...Ch. 5.8 - Suppose n is an eigenvalue of the B in Exercise...Ch. 5.8 - A common misconception is that if A has a strictly...Ch. 5 - Show that if x is an eigenvector of the matrix...Ch. 5 - Suppose x is an eigenvector of A corresponding to...Ch. 5 - Use mathematical induction to show that if is an...Ch. 5 - If p(t) = c0 + c1t + c2t2 + + cntn, define p(A)...Ch. 5 - Suppose A is diagonalizable and p(t) is the...Ch. 5 - a. Let A be a diagonalizable n n matrix. Show...Ch. 5 - Show that I A is invertible when all the...Ch. 5 - Show that if A is diagonalizable, with all...Ch. 5 - Let u be an eigenvector of A corresponding to an...Ch. 5 - Let G = [AX0B] Use formula (1) for the determinant...Ch. 5 - Use Exercise 12 to find the eigenvalues of the...Ch. 5 - Use Exercise 12 to find the eigenvalues of the...Ch. 5 - Let A = [.4.3.41.2]. Explain why Ak approaches...Ch. 5 - Exercises 1923 concern the polynomial p(t) = a0 +...Ch. 5 - Exercises 1923 concern the polynomial p(t) = a0 +...Ch. 5 - Use mathematical induction to prove that for n 2,...Ch. 5 - Exercises 1923 concern the polynomial p(t) = a0 +...

Additional Math Textbook Solutions

Find more solutions based on key concepts
A box contains 3 marbles: 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble f...

A First Course in Probability (10th Edition)

Time-lagged flights An airliner passes over an airport at noon traveling 500 mi/hr due west. At l:00 P.M., anot...

Calculus: Early Transcendentals (2nd Edition)

In Exercises 11–18, find the slope of the function’s graph at the given point. Then find an equation for the li...

University Calculus: Early Transcendentals (4th Edition)

CHECK POINT I You deposit $1000 in a saving account at a bank that has a rate of 4%. a. Find the amount, A, of ...

Thinking Mathematically (6th Edition)

TRY IT YOURSELF 1 Find the mean of the points scored by the 51 winning teams listed on page 39.

Elementary Statistics: Picturing the World (7th Edition)

76. Dew Point and Altitude The dew point decreases as altitude increases. If the dew point on the ground is 80°...

College Algebra with Modeling & Visualization (5th Edition)

Knowledge Booster
Background pattern image
Algebra
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
Recommended textbooks for you
Text book image
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
Text book image
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Text book image
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Text book image
Elements Of Modern Algebra
Algebra
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Cengage Learning,
SEE MORE TEXTBOOKS
Lecture 46: Eigenvalues & Eigenvectors; Author: IIT Kharagpur July 2018;https://www.youtube.com/watch?v=h5urBuE4Xhg;License: Standard YouTube License, CC-BY
What is an Eigenvector?; Author: LeiosOS;https://www.youtube.com/watch?v=ue3yoeZvt8E;License: Standard YouTube License, CC-BY