Mathematics · Linear Algebra
Consider the two statements regarding real matrices: I. There exists a matrix N ∈ M4(ℝ) such that {(1,1,1,-1), (1,-1,1,1)} is a basis of Row(N) and (1,2,1,4) ∈ Null(N). II. There exists a matrix M ∈ M4(ℝ) such that {(1,1,1,0)T, (1,0,1,1)T} is a basis of Col(M) and {(1,1,1,1)T, (1,0,1,0)T} ⊆ Null(M). 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
Statement I is FALSE and Statement II is TRUE.
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