Problem 13. (1 point)
\begin{equation*}
\begin{Bmatrix}
\begin{bmatrix} -2\\3\\0 \end{bmatrix}, \begin{bmatrix} 6\\-1\\5 \end{bmatrix} \end{Bmatrix}
\end{equation*}
Let W be the set:
Determine if W is a basis for $\mathbb{R}^3$ and check the correct answer(s)
below.
• A. W is not a basis because it does not span $\mathbb{R}^3$.
• B. W is a basis.
• C. W is not a basis because it is linearly dependent.
Problem 14. (1 point)
Let W be the set:
$\begin{equation*}
\begin{Bmatrix}
\begin{bmatrix} 1\\0\\1 \end{bmatrix}, \begin{bmatrix} 0\\0\\0 \end{bmatrix}, \begin{bmatrix} 0\\1\\0 \end{bmatrix} \end{Bmatrix}
\end{equation*}$
Determine if W is a basis for $\mathbb{R}^3$ and check the correct answer(s)
below.
• A. W is not a basis because it does not span $\mathbb{R}^3$.
• B. W is a basis.
• C. W is not a basis because it is linearly dependent.
Problem 15. (1 point)
Determine whether the following statements are True or False.
?1. A basis is a spanning set that is as large as possible.
?2. If H = span\{$v_1,..., v_p$\}, then \{$v_1,..., v_p$\} is a basis for H
?3. A single nonzero vector by itself is linearly dependent.
?4. The columns of an invertible n x n matrix form a basis for
$\mathbb{R}^n$.
