Question

Let u and a be vectors. Is u in the plane spanned by the columns of a? Why or why not?

Answer 1

To determine if a vector u is in the plane spanned by the columns of vector a, we need to check if u can be written as a linear combination of the columns of a.

Step-by-step explanation:

In order to determine if a vector u is in the plane spanned by the columns of vector a, we need to check if vector u can be written as a linear combination of the columns of vector a.

If u can be written as a linear combination of the columns of a, then it is in the plane spanned by the columns of a. Otherwise, it is not.

To determine if u can be written as a linear combination of the columns of a, we can set up the following equation: au = c1a1 + c2a2 + ... + cnan, where c1, c2, ..., cn are scalars and a1, a2, ..., an are the column vectors of a.

If this equation has a solution for the scalars c1, c2, ..., cn, then u is in the plane spanned by the columns of a. Otherwise, it is not.