Answer:
[tex]A= \left[\begin{array}{ccc}1&1&1\\1&1&1\\1&1&1\end{array}\right][/tex] and [tex]b=(1,0,0)[/tex]
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 [tex]\mathbb{R}^3[/tex] and there would not be such b).
Consider the vector [tex]b=(1,0,0)[/tex] and the 3x3 matrix
[tex]\left[\begin{array}{ccc}1&1&1\\1&1&1\\1&1&1\end{array}\right][/tex]
Then, the set spanned by the columns is
[tex]span{(1,1,1)}=[/tex]{[tex]\lambda (1,1,1): \lambda \in \mathbb{R}[/tex]}
So,
[tex]b \notin span(1,1,1)[/tex] as we wanted.
