Construct a 3 x 3 matrix a, with nonzero entries, and a vector b in r3 such that b is not in the set spanned by the columns of a.

and

Step-by-step explanation:

You can choose a 3x3 matrix whose colums are not linearly independet. (observe that if you choose 3 independet vectors as columns of your matrix, the set spanned by the colums will be and there would not be such b).

Consider the vector and the 3x3 matrix

Then, the set spanned by the columns is

{}

So,

as we wanted.