Question-4

\(S\) is a linearly independent subset of \(\mathbb{R}^{4}\). Select all true statements concerning \(S\).

• \(|S| \leqslant 4\)

• Any subset of \(S\) is also a linearly independent subset of \(\mathbb{R}^{4}\).

• Any superset of \(S\) is also a linearly independent subset of \(\mathbb{R}^{4}\).

• \(S\) is a basis for \(\mathbb{R}^{4}\).

NoteAnswer

• \(|S| \leqslant 4\)

• Any subset of \(S\) is also a linearly independent subset of \(\mathbb{R}^{4}\).

• Any superset of \(S\) is also a linearly independent subset of \(\mathbb{R}^{4}\).

• \(S\) is a basis for \(\mathbb{R}^{4}\).

NoteSolution

\(S\) will be a basis for \(\mathbb{R}^{4}\) if and only if \(|S| = 4\).