ppose the columns of a matrix A = a₁ oose the correct answer below. ap are linearly independent. Explain why {a₁,..., ap} is a basis for Col A. A. Since Col A is the set of all linear combinations of a₁,... ap the pivot columns of matrix A form a basis for Col A. Therefore, {a₁,..., ap) is a bas B. Since Col A is the set of all linear combinations of a₁, ... ap, the set (a₁,..., ap} spans Col A. Because (a₁, . Col A. ap} is linearly dependent, it is a C. Since Col A is the set of all linear combinations of a₁,..., ap, the set (a₁, ..., ap} spans Col A. Because (a₁, for Col A. **** ap} is also linearly independent D. Since Col A is the set of all linear combinations of a₁,..., ap the pivot columns of matrix A do not form a basis for Col A. Therefore, {a₁...., ap Col A.
ppose the columns of a matrix A = a₁ oose the correct answer below. ap are linearly independent. Explain why {a₁,..., ap} is a basis for Col A. A. Since Col A is the set of all linear combinations of a₁,... ap the pivot columns of matrix A form a basis for Col A. Therefore, {a₁,..., ap) is a bas B. Since Col A is the set of all linear combinations of a₁, ... ap, the set (a₁,..., ap} spans Col A. Because (a₁, . Col A. ap} is linearly dependent, it is a C. Since Col A is the set of all linear combinations of a₁,..., ap, the set (a₁, ..., ap} spans Col A. Because (a₁, for Col A. **** ap} is also linearly independent D. Since Col A is the set of all linear combinations of a₁,..., ap the pivot columns of matrix A do not form a basis for Col A. Therefore, {a₁...., ap Col A.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose the columns of a matrix A = a₁ ap are linearly independent. Explain why {a₁,
Choose the correct answer below.
ap is a basis for Col A.
O A. Since Col A is the set of all linear combinations of a₁, ..., ap, the pivot columns of matrix A form a basis for Col A. Therefore, (a₁, ..., ap} is a basis for Col A.
OB. Since Col A is the set of all linear combinations of a₁,..., ap, the set (a₁,..., ap} spans Col A. Because (a₁, ..., ap} is linearly dependent, it is a basis for
Col A.
OC. Since Col A is the set of all linear combinations of a₁, ..., ap, the set (a₁,..., i
for Col A.
ap} spans Col A. Because (a₁, ..., ap) is also linearly independent, it is a basis
O D. Since Col A is the set of all linear combinations of a₁,..., ap, the pivot columns of matrix A do not form a basis for Col A. Therefore, (a₁,..., ap) is a basis for
Col A.
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