Practice Consistency Of A System (21.1.4) - Linear Algebra

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6 sample questions

Question 1.
Define a consistent system of linear equations.
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Think about what it means for equations to intersect.
Question 2.
What is an inconsistent system?
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Consider what happens when two lines are parallel.
3Question 3.
What type of system has at least one solution?
- Inconsistent
- Consistent
- Infinite
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Think about what happens when lines intersect.
4Question 4.
True or False: An inconsistent system has no solutions.
- True
- False
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Remember the definition of inconsistency.
Question 5.
Given the equations x + y = 4 and 2x + 2y = 8, determine the consistency of this system and explain why.
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Graph the equations or manipulate them algebraically.
Question 6.
If a system has three variables (x, y, z), but only one equation, explain the implications for consistency.
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Consider how the lack of constraints affects solutions.

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