To decide: if the given statement is true or false.

Question

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Answer 1

Question

Chapter 7, Problem 1SE

To determine

To decide: if the given statement is true or false.

Expert Solution & Answer

Answer to Problem 1SE

True.

Explanation of Solution

Given information:

The statement, “If A is orthogonally diagonalizable, then A is symmetric.”

Theorem Used:

An n×n matrix A is orthogonally diagonalizable if and only if A is a symmetric matrix.

The given statement is true.

By the above theorem, it is clear that since the matrix A is orthogonally diagonalizable, so it must also be symmetric.

Hence, given statement is true.

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Answer 2

Question

Chapter 7, Problem 1SE

To determine

To decide: if the given statement is true or false.

Expert Solution & Answer

Answer to Problem 1SE

True.

Explanation of Solution

Given information:

The statement, “If A is orthogonally diagonalizable, then A is symmetric.”

Theorem Used:

An n×n matrix A is orthogonally diagonalizable if and only if A is a symmetric matrix.

The given statement is true.

By the above theorem, it is clear that since the matrix A is orthogonally diagonalizable, so it must also be symmetric.

Hence, given statement is true.

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Answer 3

Question

Chapter 7, Problem 1SE

To determine

To decide: if the given statement is true or false.

Expert Solution & Answer

Answer to Problem 1SE

True.

Explanation of Solution

Given information:

The statement, “If A is orthogonally diagonalizable, then A is symmetric.”

Theorem Used:

An n×n matrix A is orthogonally diagonalizable if and only if A is a symmetric matrix.

The given statement is true.

By the above theorem, it is clear that since the matrix A is orthogonally diagonalizable, so it must also be symmetric.

Hence, given statement is true.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 7, Problem 1SE

To determine

To decide: if the given statement is true or false.

Expert Solution & Answer

Answer to Problem 1SE

True.

Explanation of Solution

Given information:

The statement, “If A is orthogonally diagonalizable, then A is symmetric.”

Theorem Used:

An n×n matrix A is orthogonally diagonalizable if and only if A is a symmetric matrix.

The given statement is true.

By the above theorem, it is clear that since the matrix A is orthogonally diagonalizable, so it must also be symmetric.

Hence, given statement is true.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 7, Problem 1SE

To determine

To decide: if the given statement is true or false.

Expert Solution & Answer

Answer to Problem 1SE

True.

Explanation of Solution

Given information:

The statement, “If A is orthogonally diagonalizable, then A is symmetric.”

Theorem Used:

An n×n matrix A is orthogonally diagonalizable if and only if A is a symmetric matrix.

The given statement is true.

By the above theorem, it is clear that since the matrix A is orthogonally diagonalizable, so it must also be symmetric.

Hence, given statement is true.

Answer 6

Chapter 7, Problem 1SE

To determine

To decide: if the given statement is true or false.

Expert Solution & Answer

Answer to Problem 1SE

True.

Explanation of Solution

Given information:

The statement, “If A is orthogonally diagonalizable, then A is symmetric.”

Theorem Used:

An n×n matrix A is orthogonally diagonalizable if and only if A is a symmetric matrix.

The given statement is true.

By the above theorem, it is clear that since the matrix A is orthogonally diagonalizable, so it must also be symmetric.

Hence, given statement is true.

Answer 7

Chapter 7, Problem 1SE

To determine

To decide: if the given statement is true or false.

Answer 8

Expert Solution & Answer

Answer to Problem 1SE

True.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given information:

The statement, “If A is orthogonally diagonalizable, then A is symmetric.”

Theorem Used:

An n×n matrix A is orthogonally diagonalizable if and only if A is a symmetric matrix.

The given statement is true.

By the above theorem, it is clear that since the matrix A is orthogonally diagonalizable, so it must also be symmetric.

Hence, given statement is true.

Answer 12

To decide: if the given statement is true or false.

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To decide: if the given statement is true or false.

Answer to Problem 1SE

Explanation of Solution

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Chapter 7 Solutions