If the vectors $\vec w_1$, $\vec w_2$, $\vec w_3$ are linearly independent, are vectors $\vec w_1$, $\vec w_1 + \vec w_2$, $\vec w_1 + \vec w_2 + \vec w_3$ linearly independent as well? Explain
At first I thought the second set of vectors would not be linearly independent, since you are adding the components of one vector(s) onto another. However when I try to write one vector as a scalar multiple of the others, I can't seem to find any ways to do so. I tried to do the guess and check method to find situations where the vectors are linearly dependent but failed. Can anyone please put me on the right direction for explaining whether or not the new set of vectors is linearly independent or not? Thank you very much!