Concept explainers
In Exercises 21 and 22, mark each statement True or False. Justify each answer.
22. a. A linearly independent set in a subspace H is a basis for H.
b. If a finite set S of nonzero
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.
Trending nowThis is a popular solution!
Learn your wayIncludes step-by-step video
Chapter 4 Solutions
Linear Algebra and Its Applications (5th Edition)
Additional Math Textbook Solutions
College Algebra (6th Edition)
Intermediate Algebra (7th Edition)
Elementary and Intermediate Algebra
A Graphical Approach to College Algebra (6th Edition)
Introductory and Intermediate Algebra for College Students (5th Edition)
- Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set {v12v2,2v23v3,3v3v1} linearly dependent or linearly independent? Explain.arrow_forwardFind a basis for R3 that includes the vector (1,0,2) and (0,1,1).arrow_forwardUse the method of Example 2.23 and Theorem 2.6 to determine if the sets of vectors in Exercises 22-31 are linearly independent. If, for any of these, the answer can be determined by inspection (i.e., without calculation), state why. For any sets that are linearly dependent, find a dependence relationship among the vectors. [012],[213],[201]arrow_forward
- Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors {vu,wv,uw} is linearly independent or linearly dependent.arrow_forwardLet A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many vectors are in a basis for the row space of A? c How many vectors are in a basis for the column space of A? d Which vector space Rk has the row space as a subspace? e Which vector space Rk has the column space as a subspace?arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage