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Nonzero collinear vectors span a line, because their linear combinations can only reach points along that single shared line. An all-zero set spans only the origin, as any linear combination of zero vectors results in the zero vector.

Conditions: For the first case, the vectors are nonzero and collinear.; For the second case, all vectors in the set are the zero vector.

Nonzero collinear vectors span a line, because their linear combinations can only reach points along that single shared line. An all-zero set spans only the origin, as any linear combination of zero vectors results in the zero vector.

Conditions: For the first case, the vectors are nonzero and collinear.; For the second case, all vectors in the set are the zero vector.