1. $\vec{v_1}, \vec{v_2}, \dots, \vec{v_k}$ are vectors in $\mathbb{R}^n$
There is a unique soln to $A\vec{x} = \vec{0}$ where $A = [\vec{v_1} \vec{v_2} \dots \vec{v_k}]$
a) Is the set $\{\vec{v_1}, \vec{v_2}, \dots, \vec{v_k}\}$ linearly dependent/independent? Explain.
b) Is the set $\{2\vec{v_2}, 3\vec{v_3}, \dots, k\vec{v_k}\}$ linearly dependent/independent? Explain.
(Note: The text "no $\vec{v_1}$ + other $\vec{v_i}$ is multiplied by i" seems to be a handwritten note or a correction, not part of the original question statement for part b).
