Let A be an m × m matrix with real entries and let x be an m × 1 vector of unknowns. Consider the two statements given below: I: There exists a non-zero vector b1 ∈ ℝm such that the linear system Ax = b1 has NO solution. II: There exist non-zero vectors b2, b3 ∈ ℝm, with b2 ≠ cb3 for any c ∈ ℝ, such that the linear systems Ax = b2 and Ax = b3 have solutions. Which of the following statements is true?

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Mathematics · Linear Algebra

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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Both I and II can be TRUE simultaneously

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Answer 1

If m = 2, then at least one of I and II is FALSE

Answer 2

Both I and II can be TRUE simultaneously

Answer 3

I is TRUE whenever A is singular

Answer 4

II is TRUE whenever A is singular

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