Explanation Approach: If there are two matrix A = [ a i j ] r 1 × c 1 and B = [ b i j ] r 2 × c 2 A = [ a 11 a 12 a 13 a 21 a 22 a 23 ] 2 × 3 and B = [ b 11 b 12 b 21 b 22 b 31 b 33 ] 3 × 2 The multiplication of two given matrix: A B = [ a 11 a 12 a 13 a 21 a 22 a 23 ] 2 × 3 [ b 11 b 12 b 21 b 22 b 31 b 33 ] 3 × 2 = [ a 11 ( b 11 ) a 12 ( b 21 ) a 13 ( b 31 ) a 21 ( b 12 ) a 22 ( b 22 ) a 23 ( b 33 ) ] 3 × 3 A square matrix A with a real element said to be orthogonal if it satisfied following condition 1: A T = A − 1 2: A A T = A T A = I The set of column vector { P 1 , P 2 , P 3 , … P n } said to be orthogonal if it satisfied following condition. P i ⋅ P j = 0 , i ≠ j and P i ⋅ P j = ‖ P ‖ 2 = 1 Calculation: Consider the given matrix: A = [ 1 10 10 0 0 − 3 10 10 0 0 1 0 0 1 0 0 3 10 10 0 0 1 10 10 ] Calculate the transpose of above matrix by interchange row and column: A T = [ 1 10 10 0 0 3 10 10 0 0 1 0 0 1 0 0 − 3 10 10 0 0 1 10 10 ] Calculate the product of matrix A and A T : A A T = [ 1 10 10 0 0 − 3 10 10 0 0 1 0 0 1 0 0 3 10 10 0 0 1 10 10 ] [ 1 10 10 0 0 3 10 10 0 0 1 0 0 1 0 0 − 3 10 10 0 0 1 10 10 ] = [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] The product of the matrix A and A T is identity

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN: 9781305658004

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 7.3, Problem 32E

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Whether the matrix [1101000−3101000100100310100011010] is orthogonal or not. If the matrix is orthogonal then show that the column vectors of the matrix form an orthonormal set.

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Chapter 7.3, Problem 31E

Chapter 7.3, Problem 33E

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Chapter 7 Solutions

Elementary Linear Algebra (MindTap Course List)

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,...

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To check: Whether the matrix [ 1 10 10 0 0 − 3 10 10 0 0 1 0 0 1 0 0 3 10 10 0 0 1 10 10 ] is orthogonal or not. If the matrix is orthogonal then show that the column vectors of the matrix form an orthonormal set.

Solution Summary: The author explains that the given matrix is orthogonal and the column vectors of the matrix form an orthonormal set.

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To check:

Whether the matrix [1101000−3101000100100310100011010] is orthogonal or not. If the matrix is orthogonal then show that the column vectors of the matrix form an orthonormal set.

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Chapter 7 Solutions

To check: Whether the matrix [ 1 10 10 0 0 − 3 10 10 0 0 1 0 0 1 0 0 3 10 10 0 0 1 10 10 ] is orthogonal or not. If the matrix is orthogonal then show that the column vectors of the matrix form an orthonormal set.

Solution Summary: The author explains that the given matrix is orthogonal and the column vectors of the matrix form an orthonormal set.

Videos

To check: Whether the matrix [1101000−3101000100100310100011010] is orthogonal or not. If the matrix is orthogonal then show that the column vectors of the matrix form an orthonormal set.

Want to see the full answer?

Chapter 7 Solutions

To check:

Whether the matrix [1101000−3101000100100310100011010] is orthogonal or not. If the matrix is orthogonal then show that the column vectors of the matrix form an orthonormal set.