the correct answers for individual parts.
1. The set \begin{Bmatrix} \begin{bmatrix} 1\\2\\3\\4 \end{bmatrix}, \begin{bmatrix} -5\\2\\1\\3 \end{bmatrix}, \begin{bmatrix} 0\\1\\0\\1 \end{bmatrix}, \begin{bmatrix} 2\\2\\2\\2 \end{bmatrix}, \begin{bmatrix} -1\\0\\-3\\0 \end{bmatrix} \end{Bmatrix} is a basis of \mathbb{R}^4.
True
False
2. The set \begin{Bmatrix} \begin{bmatrix} 0\\0\\0 \end{bmatrix} \end{Bmatrix} is a subspace of \mathbb{R}^3.
True
False
3. If A is invertible, then the set of vectors made of the columns of A is linearly independent.
True
False
4. The set \begin{Bmatrix} \begin{bmatrix} 1\\1\\0 \end{bmatrix}, \begin{bmatrix} 1\\0\\1 \end{bmatrix}, \begin{bmatrix} 0\\1\\1 \end{bmatrix} \end{Bmatrix} is a basis of \mathbb{R}^3.
