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The number of variable A plane in R³ is a two The dimension of the

The number of variable A plane in R³ is a two The dimension of the

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 21EQ
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Suppose that V is vector space and A is an m x n matrix. Which of the following statements is true? The number of variables in the equation Ax O equals the nullity A A plane in R³ is a two dimensional subspace of R³ The dimension of the vector space Ps is 5 The number of pivot columns of a matrix equals the dimension of its column space or row space None of these is true
Transcribed Image Text:Suppose that V is vector space and A is an m x n matrix. Which of the following statements is true? The number of variables in the equation Ax O equals the nullity A A plane in R³ is a two dimensional subspace of R³ The dimension of the vector space Ps is 5 The number of pivot columns of a matrix equals the dimension of its column space or row space None of these is true
pose that Vis vector space and A is an m x n matrix. Which of the following statements is (are) true Statements A, B, D and E A)The dimension of the row space and the column space of A are the same, even if A is not a square matrix E) The nullity of A is the number of columns of A that are not pivot columns. D) If a set (V₁, V2,..., v₂} spans a finite dimensional vector space V and T is a set of more than p vectors in V. t Statements A.C.D and E C) A vector space is infinite dimensional if it is spanned by an infinite set B) Suppose that B is any echelon form of A. Then the pivot columns of B form a basis for the column space of A Statements A. B and C Statements A, D and E
Transcribed Image Text:pose that Vis vector space and A is an m x n matrix. Which of the following statements is (are) true Statements A, B, D and E A)The dimension of the row space and the column space of A are the same, even if A is not a square matrix E) The nullity of A is the number of columns of A that are not pivot columns. D) If a set (V₁, V2,..., v₂} spans a finite dimensional vector space V and T is a set of more than p vectors in V. t Statements A.C.D and E C) A vector space is infinite dimensional if it is spanned by an infinite set B) Suppose that B is any echelon form of A. Then the pivot columns of B form a basis for the column space of A Statements A. B and C Statements A, D and E
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