Determine whether the statement below is true or false. Justify the answer. If H is a p-dimensional subspace of R", then a linearly independent set of p vectors in H is a basis for H. Choose the correct answer below. O A. The statement is false. It is possible for p vectors to be linearly independent without spanning H. O B. The statement is false. This is only true if n=p. OC. The statement is false. This is only true if n p. O D. The statement is true. Any set of p linearly independent vectors is a basis for H.

Determine whether the statement below is true or false. Justify the answer. If H is a p-dimensional subspace of R", then a linearly independent set of p vectors in H is a basis for H. Choose the correct answer below. O A. The statement is false. It is possible for p vectors to be linearly independent without spanning H. O B. The statement is false. This is only true if n=p. OC. The statement is false. This is only true if n p. O D. The statement is true. Any set of p linearly independent vectors is a basis for H.

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...

See similar textbooks