Question

If v is a non-zero vector of dimension 3$\times$ 1 , then the matrix A = $v{v}^T$ has a rank

Answer 1

$\because V={\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]}_{3\times 1}\Rightarrow \rho \left(v\right)=1$

and we know that $\rho \left(v\right)=\rho \left(v{v}^T\right)=1,so\rho \left(A\right)=1also.$