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1. The standard operations in R" are vector addition and scalar nultiplication. 2. The additive inverse of a vector in not unique. 3. Elementary tow operation prewerves the column space of the matrix A. 4. A linearly independent spauning set S in the veetor space V is a basis for a vector space V. 5. If an uxn matrix A is an invertihle matrix, the the n row vectos are lineatly inde- pendent.

1. The standard operations in R" are vector addition and scalar nultiplication. 2. The additive inverse of a vector in not unique. 3. Elementary tow operation prewerves the column space of the matrix A. 4. A linearly independent spauning set S in the veetor space V is a basis for a vector space V. 5. If an uxn matrix A is an invertihle matrix, the the n row vectos are lineatly inde- pendent.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section: Chapter Questions
Problem 17RQ
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1. The standard operations in R" are veetor addition and scalar mmitiplication. 2. The additive inverse of a vector is not unique. 3. Elementary tow operation preserves the column space of the matrix A. 4. A linearly independent spaning set S in the vector space V is a basin for a vector pace V. 5. If an uxn matrix A is an invertible matrix, then the n row vectors are linearly pendent. Inde- 6. When homogeneons nystem are solved from the reduced row echelon form, the span- ning set in always linearly independent. 7. The orthogonal complement of a mhmpace of R° is a subspace R". 8. The intersection of two orthogonal subspaces of R" consists only the zero vector. 9. The angle between the zero vector and another vector is not defined. 10. If the uxm matrix A is invertible, then the rank(A) =n
Transcribed Image Text:1. The standard operations in R" are veetor addition and scalar mmitiplication. 2. The additive inverse of a vector is not unique. 3. Elementary tow operation preserves the column space of the matrix A. 4. A linearly independent spaning set S in the vector space V is a basin for a vector pace V. 5. If an uxn matrix A is an invertible matrix, then the n row vectors are linearly pendent. Inde- 6. When homogeneons nystem are solved from the reduced row echelon form, the span- ning set in always linearly independent. 7. The orthogonal complement of a mhmpace of R° is a subspace R". 8. The intersection of two orthogonal subspaces of R" consists only the zero vector. 9. The angle between the zero vector and another vector is not defined. 10. If the uxm matrix A is invertible, then the rank(A) =n
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