Let $W_{1}$ be the set: $\Bigg\lbrace \left[\begin{array}{c}1\\0\\0\\\end{array}\right], \left[\begin{array}{c}1\\1\\0\\\end{array}\right], \left[\begin{array}{c}1\\1\\1\\\end{array}\right] \Bigg\rbrace$
Determine if $W_{1}$ is a basis for ${\mathbb R}^3$ and check the correct answer(s) below.

A. $W_{1}$ is not a basis because it is linearly dependent.
B. $W_{1}$ is not a basis because it does not span ${\mathbb R}^3$.
C. $W_{1}$ is a basis.


Let $W_{2}$ be the set: $\Bigg\lbrace \left[\begin{array}{c}1\\0\\1\\\end{array}\right], \left[\begin{array}{c}0\\0\\0\\\end{array}\right], \left[\begin{array}{c}0\\1\\0\\\end{array}\right] \Bigg\rbrace$
Determine if $W_{2}$ is a basis for ${\mathbb R}^3$ and check the correct answer(s) below.

A. $W_{2}$ is not a basis because it is linearly dependent.
B. $W_{2}$ is not a basis because it does not span ${\mathbb R}^3$.
C. $W_{2}$ is a basis.