We are given a set of vectors: $\left[{\begin{matrix}5 \cr 2 \cr 3 \cr 5 \cr \end{matrix}}\right]$, $\left[{\begin{matrix}10 \cr 6 \cr 1 \cr 9 \cr \end{matrix}}\right]$, $\left[{\begin{matrix}5 \cr 6 \cr -8 \cr 1 \cr \end{matrix}}\right]$, and $\left[{\begin{matrix}25 \cr 16 \cr 2 \cr 16 \cr \end{matrix}}\right]$.

We want to determine if the set is linearly independent. To do that we write the vectors as columns of a matrix $A$ and row reduce that matrix.

Choose the best answer

A. The set is linearly independent because the number of rows and columns in $A$ is the same.
B. The set is linearly independent because after row reducing matrix $A$ we get a matrix without a row of zeros.
C. The set is linearly independent because after row reducing matrix $A$ we get a matrix with a row of zeros.
D. The set is linearly dependent because after row reducing matrix $A$ we get a matrix without a row of zeros.
E. The set is linearly dependent because after row reducing matrix $A$ we get a matrix with a row of zeros.
F. The set is linearly dependent because the number of rows and columns in $A$ is the same.
G. We cannot tell if the set $\lbrace{{\bf u}, {\bf v}, {\bf w}}\rbrace$ is linearly independent or not.