(a) Whether the given matrix is symmetric or not, A = [ − 1 0 − 1 0 1 0 1 0 − 1 0 − 1 0 1 0 − 1 0 − 1 0 − 1 0 1 0 − 1 0 − 1 ]

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Answer 1

Question

Chapter 7.3, Problem 58E

To determine

(a)

Whether the given matrix is symmetric or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(b)

Whether the given matrix is diagonalizable or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(c)

Whether the eigenvalue of A real.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(d)

Whether eigenvalues of A are distinct, the dimension of the corresponding Eigen spaces.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(e)

Whether matrix A is orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(f)

Whether eigenvalues of A, are the corresponding eigenvectors orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(g)

Whether A orthogonally diagonalizable.

A=[−10−101010−10−1010−10−10−1010−10−1]

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Answer 2

Question

Chapter 7.3, Problem 58E

To determine

(a)

Whether the given matrix is symmetric or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(b)

Whether the given matrix is diagonalizable or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(c)

Whether the eigenvalue of A real.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(d)

Whether eigenvalues of A are distinct, the dimension of the corresponding Eigen spaces.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(e)

Whether matrix A is orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(f)

Whether eigenvalues of A, are the corresponding eigenvectors orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(g)

Whether A orthogonally diagonalizable.

A=[−10−101010−10−1010−10−10−1010−10−1]

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 7.3, Problem 58E

To determine

(a)

Whether the given matrix is symmetric or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(b)

Whether the given matrix is diagonalizable or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(c)

Whether the eigenvalue of A real.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(d)

Whether eigenvalues of A are distinct, the dimension of the corresponding Eigen spaces.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(e)

Whether matrix A is orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(f)

Whether eigenvalues of A, are the corresponding eigenvectors orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(g)

Whether A orthogonally diagonalizable.

A=[−10−101010−10−1010−10−10−1010−10−1]

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 7.3, Problem 58E

To determine

(a)

Whether the given matrix is symmetric or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(b)

Whether the given matrix is diagonalizable or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(c)

Whether the eigenvalue of A real.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(d)

Whether eigenvalues of A are distinct, the dimension of the corresponding Eigen spaces.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(e)

Whether matrix A is orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(f)

Whether eigenvalues of A, are the corresponding eigenvectors orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(g)

Whether A orthogonally diagonalizable.

A=[−10−101010−10−1010−10−10−1010−10−1]

Expert Solution & Answer

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See solution

Answer 5

Chapter 7.3, Problem 58E

To determine

(a)

Whether the given matrix is symmetric or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(b)

Whether the given matrix is diagonalizable or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(c)

Whether the eigenvalue of A real.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(d)

Whether eigenvalues of A are distinct, the dimension of the corresponding Eigen spaces.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(e)

Whether matrix A is orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(f)

Whether eigenvalues of A, are the corresponding eigenvectors orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

To determine

(g)

Whether A orthogonally diagonalizable.

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 6

Chapter 7.3, Problem 58E

To determine

(a)

Whether the given matrix is symmetric or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 7

Chapter 7.3, Problem 58E

To determine

(a)

Whether the given matrix is symmetric or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 8

To determine

(b)

Whether the given matrix is diagonalizable or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 9

To determine

(b)

Whether the given matrix is diagonalizable or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 10

To determine

(c)

Whether the eigenvalue of A real.

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 11

To determine

(c)

Whether the eigenvalue of A real.

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 12

To determine

(d)

Whether eigenvalues of A are distinct, the dimension of the corresponding Eigen spaces.

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 13

To determine

(d)

Whether eigenvalues of A are distinct, the dimension of the corresponding Eigen spaces.

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 14

To determine

(e)

Whether matrix A is orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 15

To determine

(e)

Whether matrix A is orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 16

To determine

(f)

Whether eigenvalues of A, are the corresponding eigenvectors orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 17

To determine

(f)

Whether eigenvalues of A, are the corresponding eigenvectors orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 18

To determine

(g)

Whether A orthogonally diagonalizable.

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 19

To determine

(g)

Whether A orthogonally diagonalizable.

A=[−10−101010−10−1010−10−10−1010−10−1]

Answer 20

Expert Solution & Answer

Answer 21

Expert Solution & Answer

Answer 22

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Answer 23

Ch. 7.1 - Verifying Eigenvalues and Eigenvectors in...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Verifying Eigenvalues and Eigenvectors in...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Determining Eigenvectors In Exercise 9-12,...Ch. 7.1 - Determining Eigenvectors In Exercise 9-12,...

(a) Whether the given matrix is symmetric or not, A = [ − 1 0 − 1 0 1 0 1 0 − 1 0 − 1 0 1 0 − 1 0 − 1 0 − 1 0 1 0 − 1 0 − 1 ]

Solution Summary: The author evaluates whether the given matrix is symmetric or not by interchanging the row and column.

Videos

(a)

Whether the given matrix is symmetric or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

(b)

Whether the given matrix is diagonalizable or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

(c)

Whether the eigenvalue of A real.

A=[−10−101010−10−1010−10−10−1010−10−1]

(d)

Whether eigenvalues of A are distinct, the dimension of the corresponding Eigen spaces.

A=[−10−101010−10−1010−10−10−1010−10−1]

(e)

Whether matrix A is orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

(f)

Whether eigenvalues of A, are the corresponding eigenvectors orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

(g)

Whether A orthogonally diagonalizable.

A=[−10−101010−10−1010−10−10−1010−10−1]

Want to see the full answer?

Chapter 7 Solutions

(a) Whether the given matrix is symmetric or not, A = [ − 1 0 − 1 0 1 0 1 0 − 1 0 − 1 0 1 0 − 1 0 − 1 0 − 1 0 1 0 − 1 0 − 1 ]

Solution Summary: The author evaluates whether the given matrix is symmetric or not by interchanging the row and column.

Videos

(a) Whether the given matrix is symmetric or not, A=[−10−101010−10−1010−10−10−1010−10−1]

(b) Whether the given matrix is diagonalizable or not, A=[−10−101010−10−1010−10−10−1010−10−1]

(c) Whether the eigenvalue of A real. A=[−10−101010−10−1010−10−10−1010−10−1]

(d) Whether eigenvalues of A are distinct, the dimension of the corresponding Eigen spaces. A=[−10−101010−10−1010−10−10−1010−10−1]

(e) Whether matrix A is orthogonal. A=[−10−101010−10−1010−10−10−1010−10−1]

(f) Whether eigenvalues of A, are the corresponding eigenvectors orthogonal. A=[−10−101010−10−1010−10−10−1010−10−1]

(g) Whether A orthogonally diagonalizable. A=[−10−101010−10−1010−10−10−1010−10−1]

Want to see the full answer?

Chapter 7 Solutions

(a)

Whether the given matrix is symmetric or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

(b)

Whether the given matrix is diagonalizable or not,

A=[−10−101010−10−1010−10−10−1010−10−1]

(c)

Whether the eigenvalue of A real.

A=[−10−101010−10−1010−10−10−1010−10−1]

(d)

Whether eigenvalues of A are distinct, the dimension of the corresponding Eigen spaces.

A=[−10−101010−10−1010−10−10−1010−10−1]

(e)

Whether matrix A is orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

(f)

Whether eigenvalues of A, are the corresponding eigenvectors orthogonal.

A=[−10−101010−10−1010−10−10−1010−10−1]

(g)

Whether A orthogonally diagonalizable.

A=[−10−101010−10−1010−10−10−1010−10−1]