25.3 - Conditions for Existence of a Solution
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Practice Questions
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What is the condition for a system of linear equations to be consistent?
💡 Hint: Think about the relationship between the ranks.
If Rank(A) is 2 and Rank([A|b]) is 2, what can we say about the system?
💡 Hint: Check how ranks relate to solutions.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What condition must hold for a linear system to have at least one solution?
💡 Hint: Think about the equality between ranks.
True or False: A system of linear equations can still be consistent if Rank(A) is less than Rank([A|b]).
💡 Hint: Recall the definition of consistency.
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Challenge Problems
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Given A = [[1, 2], [3, 6]] and b = [4, 8], find the ranks of A and [A|b], and determine the existence of a solution.
💡 Hint: Calculate the ranks step by step.
Create a system of equations where Rank(A) < Rank([A|b]) and explain why no solutions exist geometrically.
💡 Hint: Visualize the equations on a graph.
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