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.
The span of two nonzero, non-collinear vectors is the entire 2D plane. This means that by taking all possible linear combinations of these two vectors, you can reach any point in the plane.
Conditions: The two vectors are nonzero.; The two vectors are non-collinear (they do not lie on the same line).
The span of two nonzero, non-collinear vectors is the entire 2D plane. This means that by taking all possible linear combinations of these two vectors, you can reach any point in the plane.
Conditions: The two vectors are nonzero.; The two vectors are non-collinear (they do not lie on the same line).