MathAlgebraLinear algebraVectors and vector spaces

Basis of a vector space

Basis of 4-dimensional space

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Suppose we have three vectors: $x = \begin{pmatrix} 1 \\ -1 \\ 2 \\ 0\end{pmatrix}$ , $y = \begin{pmatrix} 5 \\ 4 \\ 1 \\ 8\end{pmatrix}$ and $z = \begin{pmatrix} 3 \\ -1 \\ 0 \\ 2\end{pmatrix}$ . Can this system of vectors be the basis of a 4-dimensional space?

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Yes, these vectors can be a basis of 4-dimensional space.

No, these vectors can not be a basis of 4-dimensional space.

It depends on a vector space.

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