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[All Steps] In R^3 let U_1=(1,3,4), U_2=(4,0,1), U_3=(3,1,2). Determine the dimension of span; U_1,U_2,U_3 and determine if (1,1,1,, lies in span

Question: In \(\mathbb{R}^{3}\) let \(U_{1}=(1,3,4), U_{2}=(4,0,1), U_{3}=(3,1,2)\). Determine the dimension of \(\operatorname{span}\left\{ {{U}_{1}},{{U}_{2}},{{U}_{3}} \right\}\) and determine if \((1,1,1,\), lies in span \(\left\{ {{U}_{1}},{{U}_{2}},{{U}_{3}} \right\}\)

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