Mathematics · Linear Algebra

Select the INCORRECT statement from the following options regarding vector spaces.

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1Any two non-zero vectors are linearly dependent if and only if one is a scalar multiple of the other.
2Any two vectors u, v in ℝ3 are linearly dependent if and only if they lie on the same line through the origin.
3Any two vectors u, v in ℝ3 are linearly independent if and only if they lie on the same line through the origin.✓
4Any three vectors u, v, w in ℝ3 are linearly dependent if and only if they lie on the same plane through the origin.

Correct answer

Any two vectors u, v in ℝ3 are linearly independent if and only if they lie on the same line through the origin.

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