D. The nullspace of A is a subspace of R". DE. The row space of A is the same as the column space of AT OF. Row operations preserve the linear dependence relations among the rows of A.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 67E: Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many...
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Answer D, E, and F please!

Let A be an m x n matrix. Select the correct statement(s) below.
A. Row operations preserve the linear dependence relations among the columns of A
B. The dimension of row space and the column space of A are the same, even if A is not square.
172
Oc. If A is square and rank(A) = n, then the equation Ax = b has a solution for all bin R
OD. The nullspace of A is a subspace of R TL
OE. The row space of A is the same as the column space of AT
F. Row operations preserve the linear dependence relations among the rows of A.
G. none of the above
Transcribed Image Text:Let A be an m x n matrix. Select the correct statement(s) below. A. Row operations preserve the linear dependence relations among the columns of A B. The dimension of row space and the column space of A are the same, even if A is not square. 172 Oc. If A is square and rank(A) = n, then the equation Ax = b has a solution for all bin R OD. The nullspace of A is a subspace of R TL OE. The row space of A is the same as the column space of AT F. Row operations preserve the linear dependence relations among the rows of A. G. none of the above
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D)Nullspace as a subspace of Rn (true)

 

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