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.
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The set {2, 3} cannot be a basis of â„^4 because a basis of â„^4 must have 4 vectors. Therefore, the statement is False. Show more…
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