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5 cards from this section. Quick, good the night before a test.
What is the general form of a system of linear equations?
Think about the arrangement of equations and their variables.
What does a homogeneous system mean?
Recall that there's no constant on the right-hand side.
What is the matrix form of a system of linear equations?
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.
Think about what inconsistency means in terms of rank.
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.
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.
Look for proportional relationships among the equations to determine if they are independent or not.
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