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

Chapter 5, Problem 35E

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QUESTION:

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

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QUESTION:

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

ANSWER:

Solution 35E

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

Picture 3

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