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Solved: In Exercises 21 and 22, mark each statement True
Chapter 4, Problem 22E(choose chapter or problem)
In Exercises 21 and 22, mark each statement True or False. Justify each answer.a. A linearly independent set in a subspace H is a basis for H.b. If a finite set S of nonzero vectors spans a vector space V, then some subset of S is a basis for V.c. A basis is a linearly independent set that is as large as possible.d. The standard method for producing a spanning set for Nul A, described in Section 4.2, sometimes fails to produce a basis for Nul A.e. If B is an echelon form of a matrix A, then the pivot columns of B form a basis for Col A.
Questions & Answers
QUESTION:
In Exercises 21 and 22, mark each statement True or False. Justify each answer.a. A linearly independent set in a subspace H is a basis for H.b. If a finite set S of nonzero vectors spans a vector space V, then some subset of S is a basis for V.c. A basis is a linearly independent set that is as large as possible.d. The standard method for producing a spanning set for Nul A, described in Section 4.2, sometimes fails to produce a basis for Nul A.e. If B is an echelon form of a matrix A, then the pivot columns of B form a basis for Col A.
ANSWER:Solution 22EStep 1 of 5(a)Use the definition of basis to mark the true or false to given statement.Definition of basis:A set is said to be basis for space if the set is linearly independent and spans the space.The given statement is only linearly independent, so the statement is .