Linear Algebra. Suppose that the 3x6 matrix A has a row reduced form U. Let u2, u4, and u5 be the column vectors of U that have leading ones. Are the following true:

a2, a4, and a5 form the basis of the column space of A.
a1, a3, and a6 can be be written as a linear combination of a2, a4, and a5.
a2, a4, and a5 are linearly independent
the set {a2, a4, a5, and a6} is linearly dependent.
a2, a4, and a5 span the rest of the column vectors of A.

Question

Linear Algebra. Suppose that the 3x6 matrix A has a row reduced form U. Let u2, u4, and u5 be the column vectors of U that have leading ones. Are the following true:

a2, a4, and a5 form the basis of the column space of A.
a1, a3, and a6 can be be written as a linear combination of a2, a4, and a5.
a2, a4, and a5 are linearly independent
the set {a2, a4, a5, and a6} is linearly dependent.
a2, a4, and a5 span the rest of the column vectors of A.

anonymous · Answer

also let u1, u3, and u6 be the columns of U that correspond to free variables. What are true about U?

anonymous · Answer

are the following true also?

the basis of the column space of A tells me that the column space of A is contained in R^3
the column space of A has dimension of 3