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Which of the following statements is/are true? (i) The norm of each vector in an orthogonal basis is one. (ii) Every finite dimensional inner product space has an orthonornal basis. (iii) A set S is called orthonormal if some vectors in S are unit vectors. A. Only (ii) and (iii) B. All the statements. C. Only (iii) D. Only (i) O E. Only (ii)

Which of the following statements is/are true? (i) The norm of each vector in an orthogonal basis is one. (ii) Every finite dimensional inner product space has an orthonornal basis. (iii) A set S is called orthonormal if some vectors in S are unit vectors. A. Only (ii) and (iii) B. All the statements. C. Only (iii) D. Only (i) O E. Only (ii)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 33EQ
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Which of the following statements is/are true? (i) The norm of each vector in an orthogonal basis is one. (ii) Every finite dimensional inner product space has an orthonornal basis. (iii) A set S is called orthonormal if some vectors in S are unit vectors. A. Only (ii) and (iii) B. All the statements. C. Only (iii) D. Only (i) E. Only (ii)
Transcribed Image Text:Which of the following statements is/are true? (i) The norm of each vector in an orthogonal basis is one. (ii) Every finite dimensional inner product space has an orthonornal basis. (iii) A set S is called orthonormal if some vectors in S are unit vectors. A. Only (ii) and (iii) B. All the statements. C. Only (iii) D. Only (i) E. Only (ii)
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