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3 cards from this section. Quick, good the night before a test.
What is the definition of a matrix rank?
Consider the relationship of rows and columns.
In the context of a linear system, what does an inconsistent system mean?
Think about the relationships between the equations.
What does it mean for a system to be consistent?
Recall the definitions of consistent and inconsistent systems.
True or False: If rank(A) = rank([A∨B]), the system is always consistent.
Think about what this theorem states.
Consider the system: x + y + z = 1; x + y + z = 2. Analyze the rank and determine if it is consistent. Explain why or why not.
Consider the meaning of parallel lines in a graph.
Given the equations: 3x + 4y = 5 and 6x + 8y = 10, what can you deduce about the rank and the solutions of this system?
Reflect on how multiplicative relations between equations affect rank.
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