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Let u and v be the vectors shown in the figure, and

Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald ISBN: 9780321982384 49

Solution for problem 35E Chapter 5.1

Linear Algebra and Its Applications | 5th Edition

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Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald

Linear Algebra and Its Applications | 5th Edition

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Problem 35E

Problem 35E

Let u and v be the vectors shown in the figure, and suppose u and v are eigenvectors of a 2 × 2 matrix A that correspond to eigenvalues 2 and 3, respectively. Let  be the linear transformation given by  for each x in R2, and let w = u + v. Make a copy of the figure, and on the same coordinate system, carefully plot the vectors

Step-by-Step Solution:
Step 1 of 3

Solution 35E

Plot  as 2u, since u is an eigenvector for the eigenvalue 2 and = 

Picture 3

Similarly, plot as 3v, because v is an eigenvector for the eigenvalue 3 and = v= 3v

Picture 2

Now, the plot of the vector  as shown below

Picture 1

The graph contains the vectors , , and .

Step 2 of 3

Chapter 5.1, Problem 35E is Solved
Step 3 of 3

Textbook: Linear Algebra and Its Applications
Edition: 5
Author: David C. Lay; Steven R. Lay; Judi J. McDonald
ISBN: 9780321982384

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Let u and v be the vectors shown in the figure, and