Solution Found!

Math / Linear Algebra 4 / Chapter 5.1 / Problem 4

Linear Algebra | 4th Edition | ISBN: 9780130084514 | Authors: Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence

Change Question

For each linear operator T on V, find the eigenvalues of T and an ordered basis 0 for V

Chapter 5, Problem 4

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

For each linear operator T on V, find the eigenvalues of T and an ordered basis 0 for V such that [T]/3 is a diagonal matrix. (a) V = R2 and T(a, 6) = (-2a + 36. - 10a + 96) (b) V = R3 and T(a, 6, c) = (7a - 46 + 10c, 4a - 36 + 8c, -2 a + 6 - 2c) (c) V = R3 and T(a, 6, c) = (-4a + 36 - 6c. 6a - 76 + 12c, 6a - 66 + lie) (d) V = P,(7?) and T(u.r + 6) = (-6a + 26)x + (-6a + 6) (e) V = P2(R) and T(/(x)) = x/'(x) + /(2)x + /(3) (f) V = P3(R) and T(/(x)) = f(x) + /(2)x (g) V = P3(R) and T(/(x)) = xf'(x) + f

Questions & Answers

QUESTION:

For each linear operator T on V, find the eigenvalues of T and an ordered basis 0 for V such that [T]/3 is a diagonal matrix. (a) V = R2 and T(a, 6) = (-2a + 36. - 10a + 96) (b) V = R3 and T(a, 6, c) = (7a - 46 + 10c, 4a - 36 + 8c, -2 a + 6 - 2c) (c) V = R3 and T(a, 6, c) = (-4a + 36 - 6c. 6a - 76 + 12c, 6a - 66 + lie) (d) V = P,(7?) and T(u.r + 6) = (-6a + 26)x + (-6a + 6) (e) V = P2(R) and T(/(x)) = x/'(x) + /(2)x + /(3) (f) V = P3(R) and T(/(x)) = f(x) + /(2)x (g) V = P3(R) and T(/(x)) = xf'(x) + f

ANSWER:

Step 1 of 22

Part (a)

Consider the linear operator,

Let’s assume is the standard basis, then the matrix representation of the standard basis is represented as,

Calculate the eigenvalue operator ,

Solve further as,

Hence the eigenvalues of the operator are and .

Study Tools You Might Need

Chapter: 5 Problem: 30P

Introductory Chemistry 5
Use the law of constant composition to complete the table summarizing the amounts of iron and chlorine produced upon the decomposition of several samples of iron(III) chloride.

Chapter: 7 Problem: 3

Campbell Biology 9
Which of the following factors would tend to increase membrane fluidity? a. a greater proportion of unsaturated phospholipids b. a greater proportion of saturated phospholipids c. a lower temperature d. a relatively high protein content in the membrane e. a greater proportion of relatively large glyc

Chapter: 0 Problem: 2

Biology 8
Which structure is not part ofthe endomembrane system? a. nuclear envelope d. plasma membrane b. chloroplast e. ER c. Golgi apparatus

Chapter: 19 Problem: 8

Glencoe Accounting: First Year Course, Student Edition 1
Completing a Worksheet and Financial Statements The trial balance for Cycle Tech Bicycles, prepared on a ten-column work sheet, is included in your working papers. Instructions 1. Complete the work sheet for the year ended December 31. Use the following information to make the adjustments.

Chapter: 17 Problem: 6

Human Anatomy & Physiology 9
The white blood cell that releases histamine and other inflammatory chemicals is the (a) basophil, (b) neutrophil, (c) monocyte, (d) eosinophil.

Chapter: 14 Problem: 14

Essentials of Statistics for the Behavioral Sciences 10
It appears that there is a significant relationship between cognitive ability and social status, at least for birds. Boogert, Reader, and Laland (2006) measured social status and individual learning ability for a group of starlings. The following data represent results similar to those obtained in th

Chapter: 6 Problem: 3

Biology: Concepts and Applications 10
In plants, photosynthetic eukaryotes, and cyanobacteria, the light-dependent reactions proceed in/at the _____ . a. thylakoid membrane b. plasma membrane c. stroma d. cytoplasm

Chapter: 18 Problem: 4

Biology for AP Courses
Which is an example of an adaptation? a. The better nutrition of a human helps her grow taller. b. The webbed feet of a duck help it swim. c. The urban location of a raccoon helps it find food. d. The large leaves of a desert plant require more water.

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account