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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the condition for a system of linear equations to be consistent?
💡 Hint: Think about the relationship between the ranks.
Question 2
Easy
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.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What condition must hold for a linear system to have at least one solution?
- Rank(A) ≠ Rank([A|b])
- Rank(A) = Rank([A|b])
- Rank(A) > Rank([A|b])
💡 Hint: Think about the equality between ranks.
Question 2
True or False: A system of linear equations can still be consistent if Rank(A) is less than Rank([A|b]).
- True
- False
💡 Hint: Recall the definition of consistency.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation