25.1 - System of Linear Equations
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Practice Questions
Test your understanding with targeted questions
What is the general form of a system of linear equations?
💡 Hint: Think about the arrangement of equations and their variables.
What does a homogeneous system mean?
💡 Hint: Recall that there's no constant on the right-hand side.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the matrix form of a system of linear equations?
💡 Hint: Recall how we express our equations in one compact form.
True or False: A system with Rank(A) < Rank([A∨b]) has infinitely many solutions.
💡 Hint: Think about what inconsistency means in terms of rank.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Analyze the following system:
3x + 4y - z = 10
2x - 2y + 5z = 5
x - 0.5y + z = 1
Determine if the system is consistent, independent, or dependent, and explain your reasoning.
💡 Hint: Consider reducing the system to find its rank and see if the equations give distinct information.
Given the complex system below, establish its characteristics:
1x + 2y + 3z = 6
4x + 5y + 6z = 15
2x + 4y + 6z = 10
Is it independent, dependent, or inconsistent? Provide rationale.
💡 Hint: Look for proportional relationships among the equations to determine if they are independent or not.
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