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Column space of $$$\left[\begin{array}{cc}7 & 0\\24 & 1\end{array}\right]$$$
Related calculator: Row Space Calculator
Your Input
Find the column space of $$$\left[\begin{array}{cc}7 & 0\\24 & 1\end{array}\right]$$$.
Solution
The reduced row echelon form of the matrix is $$$\left[\begin{array}{cc}1 & 0\\0 & 1\end{array}\right]$$$ (for steps, see rref calculator).
The column space is a space spanned by the columns of the initial matrix that correspond to the pivot columns of the reduced matrix.
Thus, the column space is $$$\left\{\left[\begin{array}{c}7\\24\end{array}\right], \left[\begin{array}{c}0\\1\end{array}\right]\right\}$$$.
Answer
The column space of the matrix is $$$\left\{\left[\begin{array}{c}7\\24\end{array}\right], \left[\begin{array}{c}0\\1\end{array}\right]\right\}$$$A.