22.7.1 - Theorem: Rouché–Capelli Theorem
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Practice Questions
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Define the Rouché–Capelli Theorem.
💡 Hint: Focus on the relationship between ranks.
What does it mean if rank(A) ≠ rank([A∨B])?
💡 Hint: Think about non-matching conditions.
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Interactive Quizzes
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What does the Rouché–Capelli Theorem determine?
💡 Hint: Focus on what the theorem facilitates.
True or False: If rank(A) = 3 and rank([A∨B]) = 3, the system has no solutions.
💡 Hint: Think about the implications of rank equality.
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Challenge Problems
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Given the system: 3x + 2y = 5, 6x + 4y = 10, analyze whether the system is consistent or inconsistent and find the nature of the solutions.
💡 Hint: Look for rank similarity in matrix forms.
A matrix A has rank 4 and is used in a system of 6 variables. Determine the type of solution the system provides.
💡 Hint: Recall how ranks impact solution types.
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