Let ${\bf u} = \left[{\begin{matrix}2 \cr 3 \cr 4 \cr \end{matrix}}\right]$, ${\bf v} = \left[{\begin{matrix}4 \cr 9 \cr 10 \cr \end{matrix}}\right]$, and ${\bf w} = \left[{\begin{matrix}2 \cr 18 \cr 14 \cr \end{matrix}}\right]$.

We want to determine if $\lbrace{{\bf u}, {\bf v}, {\bf w}}\rbrace$ 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 $\lbrace{{\bf u}, {\bf v}, {\bf w}}\rbrace$ is linearly dependent because after row reducing matrix $A$ we get a matrix without a row of zeros.
B. The set $\lbrace{{\bf u}, {\bf v}, {\bf w}}\rbrace$ is linearly independent because the number of rows and columns in $A$ is the same.
C. The set $\lbrace{{\bf u}, {\bf v}, {\bf w}}\rbrace$ is linearly independent because after row reducing matrix $A$ we get a matrix with a row of zeros.
D. The set $\lbrace{{\bf u}, {\bf v}, {\bf w}}\rbrace$ is linearly independent because after row reducing matrix $A$ we get a matrix without a row of zeros.
E. The set $\lbrace{{\bf u}, {\bf v}, {\bf w}}\rbrace$ is linearly dependent because after row reducing matrix $A$ we get a matrix with a row of zeros.
F. The set $\lbrace{{\bf u}, {\bf v}, {\bf w}}\rbrace$ 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.