(Solved): Let \( X_{1}=\left(\begin{array}{c}1 \\ -2 \\ 1 \\ 3\end{array}\right), X_{2} ...

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Let \( X_{1}=\left(\begin{array}{c}1 \\ -2 \\ 1 \\ 3\end{array}\right), X_{2}=\left(\begin{array}{c}2 \\ 1 \\ -3 \\ 1\end{array}\right) \in R^{4} \) Find: a) Dimension and a linear subspace basis \( \mathrm{L}=\mathrm{L}\left(\mathrm{x}_{1}, \mathrm{x}_{2}\right) \) generated by \( \mathrm{x}_{1} \) and \( \mathrm{x}_{2} \). b)In L, build an orthogonal base. c) Complement this basis in L to an orthonormal basis of all linear space \( R^{4} \).