The number of variable A plane in R³ is a two The dimension of the
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbeac6eb9-1fb3-41fc-a4cb-d4256681ff25%2F89cae90e-3828-4e62-b1df-2b42a7fed7ab%2F3cl2nkd_processed.jpeg&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbeac6eb9-1fb3-41fc-a4cb-d4256681ff25%2F89cae90e-3828-4e62-b1df-2b42a7fed7ab%2Fj54865_processed.jpeg&w=3840&q=75)
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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