Science:Math Exam Resources/Courses/MATH152/April 2022/Question A15/Hint 1

If ${\textstyle A}$ has 2 linearly independent eigenvectors corresponding to ${\textstyle \lambda =1}$, then the null-space of $A-\lambda I$ must be 2-dimensional; equivalently, we must have ${\textstyle \mathbf {rank} (A-\lambda I)=1}$. Is there a simple way to pick ${\textstyle b}$ so that ${\textstyle \mathbf {rank} (A-\lambda I)=1}$?