Find A such that the given set is Col A. $\{\begin{bmatrix}2s+3t\\r+s-2t\\4r+s\\3r-s-t\end{bmatrix}:r,s,t\ gamomaniea1 2021-11-19 Answered Find A such that the given set is Col A. \[\{\begin{bmatrix}2s+3t\\r+s-2t\\4r+s\\3r-s-t\end{bmatrix}:r,s,t\ real\}$

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Donald Proulx
An element in this set may be written as
$\begin{bmatrix}2s+3t\\r+s-2t\\4r+s\\3r-s-t\end{bmatrix}=r\begin{bmatrix}0\\1\\4\\3\end{bmatrix}+s\begin{bmatrix}2\\1\\1\\-1\end{bmatrix}+t\begin{bmatrix}3\\-2\\0\\-1 \end{bmatrix}=\begin{bmatrix}0&2&3\\1&1&-2\\4&1&0\\3&-1&-1 \end{bmatrix}\begin{bmatrix}r\\ s\\ t \end{bmatrix}$
where r, s and t are any real numbers. So the set is Col A where
$A=\begin{bmatrix}0&2&3\\1 & 1&-2\\4&1&0\\3&-1&-1 \end{bmatrix}$
Result:
$A=\begin{bmatrix}0&2&3\\1 & 1&-2\\4&1&0\\3&-1&-1 \end{bmatrix}$