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Let \(\mathcal{S} \subset \mathbb{R}^{4}\) be the vectors \(X=\left(x_{1}, x_{2}, x_{3}, x_{4}\right)\) that satisfy \(x_{1}+x_{2}-x_{3}+x_{4}=0\).

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Let \(\mathcal{S} \subset \mathbb{R}^{4}\) be the vectors \(X=\left(x_{1}, x_{2}, x_{3}, x_{4}\right)\) that satisfy \(x_{1}+x_{2}-x_{3}+x_{4}=0\).
a) What is the dimension of \(\mathcal{S}\) ?
b) Find a basis for the orthogonal complement of \(\mathcal{S}\).
in Mathematics by Platinum (101k points) | 314 views

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