1d310f…: “Against the autumn angle”

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True/False: Let $A$ be any $m\times n$ matrix, then $\vec {0}$ is in $\Nul A$ .

True False

True/False: Let $A$ be any $m\times n$ matrix, then $\vec {0}$ is in $\Col A$ .

True False

True/False: Let $A$ be any $m\times n$ matrix, then $\Col A = \text {Span}\{\vec {a}_1,\dots , \vec {a}_n\}$ where $A = [\vec {a}_1,\dots , \vec {a}_n]$ .

True False

True/False: Let $A$ be any $m\times n$ matrix, then $\Col A$ is a subspace of $\RR ^n$

True False

True/False: Let $A$ be any $m\times n$ matrix, then $\Col A$ is a subspace of $\RR ^m$

True False

True/False: Let $A$ be any $m\times n$ matrix, then $\Nul A$ is a subspace of $\RR ^m$

True False

True/False: Let $A$ be any $m\times n$ matrix, then $\Nul A$ is a subspace of $\RR ^n$

True False

True/False: Let $A$ be any $m\times n$ matrix, then $A$ is $\RR ^m$

True False

Suppose $\begin {bmatrix} 1\\2\end {bmatrix}$ is a solution to $A\vec {x} = \vec {0}$ where $A$ is a $5\times 2$ matrix. Is $\begin {bmatrix} 1\\2\end {bmatrix}$ in $\Nul A$ ?

Yes No Not enough information given to determine

Suppose $A\begin {bmatrix} 1\\4\end {bmatrix} = \begin {bmatrix} 5\\6\\7\end {bmatrix}$ . Which of the following statements is true?

$\begin {bmatrix} 1\\4\end {bmatrix}\in \Col A$ $\begin {bmatrix} 5\\6\\7\end {bmatrix}\in \Nul A$ $\begin {bmatrix} 5\\6\\7\end {bmatrix}\in \Col A$