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 forCol A.OC. Since Col A is the set of all linear combinations of a₁, ..., ap, the set (a₁,..., ifor Col A.ap} spans Col A. Because (a₁, ..., ap) is also linearly independent, it is a basisO 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 forCol A.

Basis of matrix A : The columns of matrix forms pivot columns of matrix A are the basis for 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.