Mathematics · Linear Algebra
Let S = {u 1 , ..., u k } be a subset of non-zero vectors from ℝ n . Consider the two statements given below: I: If S is a linearly dependent set in ℝ n , then u k is a linear combination of u 1 , ..., u k-1 . II: If S is a linearly independent set in ℝ n , then k < n. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Both Statement I and Statement II are TRUE
- 2Both Statement I and Statement II are FALSE✓
- 3Statement I is TRUE and Statement II is FALSE
- 4Statement I is FALSE and Statement II is TRUE
Correct answer
Both Statement I and Statement II are FALSE
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