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[See Steps] Find a matrix A for which col; A is the subspace of R^4 consisting of vectors of the form

Question: Find a matrix \(A\) for which \(\operatorname{col} A\) is the subspace of \(\mathbb{R}^{4}\) consisting of vectors of the form

\[\left[\begin{array}{c} 2 s-t \\ r-s+2 t \\ 3 r+s \\ 2 r-s-t \end{array}\right], \quad r, s, t \in \mathbb{R}\]

Is this subspace equal to \(\mathbb{R}^{4} ?\)

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