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.

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Chapter2: Second-order Linear Odes
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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.
Transcribed Image Text: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.
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