Determine whether the statement below is true or false. Justify the answer. If a set of p vectors spans a p-dimensional subspace H of R", then these vectors form a basis of H. Choose the correct answer below. A. The statement is false. Although the set of vectors spans H, there is not enough information to conclude that they form a basis of H. B. The statement is true. If a set of p vectors spans a p-dimensional subspace H of R", then these vectors must be linearly independent. Any linearly independent spanning set of p vectors forms a basis in p dimensions. O c. The statement is true. Any spanning set in H will form a basis of H. O D. The statement is false. Only vectors that span H and are linearly independent will form a basis of H. Since the set contains too many vectors, the spanning set cannot possibly be linearly independent.

Determine whether the statement below is true or false. Justify the answer. If a set of p vectors spans a p-dimensional subspace H of R", then these vectors form a basis of H. Choose the correct answer below. A. The statement is false. Although the set of vectors spans H, there is not enough information to conclude that they form a basis of H. B. The statement is true. If a set of p vectors spans a p-dimensional subspace H of R", then these vectors must be linearly independent. Any linearly independent spanning set of p vectors forms a basis in p dimensions. O c. The statement is true. Any spanning set in H will form a basis of H. O D. The statement is false. Only vectors that span H and are linearly independent will form a basis of H. Since the set contains too many vectors, the spanning set cannot possibly be linearly independent.

Name: See picture Determine whether the statement below is true or false. Ju
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Description: See picture Determine whether the statement below is true or false. Justify the answer.If a set of p vectors spans a p-dimensional subspace H of R", then these vectors form a basis of H.Choose the correct answer below.A. The statement is false. Altho

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 46E

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