Mathematics · Linear Algebra
Let V be a finite dimensional vector space over a field F, and let S be a nonempty subset of V. Which of the following is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If S is linearly independent, then S is a basis of V.
- 2If the linear span of S is V, then S is linearly independent.
- 3If S is linearly independent, then S contains a basis of V.
- 4If the linear span of S is V, then S contains a basis of V.✓
Correct answer
If the linear span of S is V, then S contains a basis of V.
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