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Multiple choice. Choose the correct answer without giving a reason 1. The following are the properties of the linear operator T in Rn which is one-to-one (injective) EXCEPT....... a. T onto (surjective) b. [T]¹=[T¹] c. T isomorphism d. Nullity(T) = n e. The set of rows [T] is the basis of Rn 2. A is the set containing the vectors in the finite dimensional vector space V. Which of the following sentences is always true? a. If A is linearly independent, then A is orthogonal b. If A is orthogonal, then A is linearly independent C. If A is orthonormal, then A is linearly independent d. If A is orthonormal, then A base V 3. A is a square matrix of size nxn. The following sentences are equivalent to λ are the eigenvalue of A, EXCEPT.... a. There is a nonzero vector x such that Ax =λx b. SPL Ax= x has infinitely many solutions C. det (λ- A)² > 0 d. SPL (A-AI)x= 0 has a nontrivial solution e. det(A) det(AI)

Multiple choice. Choose the correct answer without giving a reason 1. The following are the properties of the linear operator T in Rn which is one-to-one (injective) EXCEPT....... a. T onto (surjective) b. [T]¹=[T¹] c. T isomorphism d. Nullity(T) = n e. The set of rows [T] is the basis of Rn 2. A is the set containing the vectors in the finite dimensional vector space V. Which of the following sentences is always true? a. If A is linearly independent, then A is orthogonal b. If A is orthogonal, then A is linearly independent C. If A is orthonormal, then A is linearly independent d. If A is orthonormal, then A base V 3. A is a square matrix of size nxn. The following sentences are equivalent to λ are the eigenvalue of A, EXCEPT.... a. There is a nonzero vector x such that Ax =λx b. SPL Ax= x has infinitely many solutions C. det (λ- A)² > 0 d. SPL (A-AI)x= 0 has a nontrivial solution e. det(A) det(AI)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 26EQ
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Multiple choice. Choose the correct answer without giving a reason 1. The following are the properties of the linear operator T in Rn which is one-to-one (injective) EXCEPT....... a. T onto (surjective) b. [T]¹=[T¹] c. T isomorphism d. Nullity(T) = n e. The set of rows [T] is the basis of Rn 2. A is the set containing the vectors in the finite dimensional vector space V. Which of the following sentences is always true? a. If A is linearly independent, then A is orthogonal b. If A is orthogonal, then A is linearly independent C. If A is orthonormal, then A is linearly independent d. If A is orthonormal, then A base V 3. A is a square matrix of size nxn. The following sentences are equivalent to λ are the eigenvalues of A, EXCEPT.... a. There is a nonzero vector x such that Ax =λx b. SPL Ax = x has infinitely many solutions C. det (λI - A)² > 0 d. SPL (A-AI)x= 0 has a nontrivial solution e. det(A) = det(λ)
Transcribed Image Text:Multiple choice. Choose the correct answer without giving a reason 1. The following are the properties of the linear operator T in Rn which is one-to-one (injective) EXCEPT....... a. T onto (surjective) b. [T]¹=[T¹] c. T isomorphism d. Nullity(T) = n e. The set of rows [T] is the basis of Rn 2. A is the set containing the vectors in the finite dimensional vector space V. Which of the following sentences is always true? a. If A is linearly independent, then A is orthogonal b. If A is orthogonal, then A is linearly independent C. If A is orthonormal, then A is linearly independent d. If A is orthonormal, then A base V 3. A is a square matrix of size nxn. The following sentences are equivalent to λ are the eigenvalues of A, EXCEPT.... a. There is a nonzero vector x such that Ax =λx b. SPL Ax = x has infinitely many solutions C. det (λI - A)² > 0 d. SPL (A-AI)x= 0 has a nontrivial solution e. det(A) = det(λ)
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