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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 28EQ: Use the method of Example 2.23 and Theorem 2.6 to determine if the sets of vectors in Exercises...
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