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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 $\operatorname{Col} A .$

a) Falseb) Truec) Trued) Falsee) False

Calculus 3

Chapter 4

Vector Spaces

Section 3

Linearly Independent Sets; Bases

Vectors

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in this problem. We're given a few statements and were asked for work. It's that where it is true or false. So the first statement, uh, schools, Because the set of backers not only should be linearly dependent, it should also coincide which age? Hey, you could check the definition off base base. Second statement is true, and I'm gonna report you refer to the, uh, spending said here. Now, the statement is statement, you see, is also true. And this time I would refer to the section named two years off a basis. Uh, Indy, begin the statement. This falls because this standard method of producing a spend settle now a is actually always Cordish iss a re nearly Bennett sent. And it actually always produces a basis for no hey and less Damon. ISS also pulls because we need Thio look at D or use the different elements or give its Collins off matrix A not the magics B, which is the Rebecca Formal, eh? Because some columns of B mike nights be in the column space. Oh, okay. So we should also we should always use the pivot columns off our orginal matrix

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