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Math / Linear Algebra and Its Applications 4 / Chapter 7.1 / Problem 40E

Linear Algebra and Its Applications | 4th Edition | ISBN: 9780321385178 | Authors: David C. Lay

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Solved: [M] Orthogonally diagonalize the matrices in

Chapter 7, Problem 40E

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QUESTION:

Problem 40E

[M] Orthogonally diagonalize the matrices in Exercises 37–40. To practice the methods of this section, do not use an eigenvector routine from your matrix program. Instead, use the program to find the eigenvalues, and, for each eigenvalue , find an orthonormal basis for , as in Examples 2 and 3

Reference Examples 2:

If possible, diagonalize the matrix

Reference Examples 3:

Questions & Answers

QUESTION:

Problem 40E

[M] Orthogonally diagonalize the matrices in Exercises 37–40. To practice the methods of this section, do not use an eigenvector routine from your matrix program. Instead, use the program to find the eigenvalues, and, for each eigenvalue , find an orthonormal basis for , as in Examples 2 and 3

Reference Examples 2:

If possible, diagonalize the matrix

Reference Examples 3:

ANSWER:

Step 1 of 4

Let be the given matrix. We use the MATLAB to produce the eigenvalues and eigenvectors of this matrix . The commands which are used in the following solution are eig and nulbasis. The command computes the three eigenvalues of and stores them in a vector ev. be the given matrix. We use the MATLAB to produce the eigenvalues and eigenvectors of this matrix . The commands which are used in the following solution are eig and nulbasis. The command computes the three eigenvalues of and stores them in a vector ev.

The given matrix is is

So from MATLAB we have that

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