Practice Conditions For Existence Of A Solution (25.3) - Solutions of Linear Systems: Existence, Uniqueness, General Form

Practice: Conditions for Existence of a Solution

Lesson 25.3Solutions of Linear Systems: Existence, Uniqueness, General Form

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8 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the condition for a system of linear equations to be consistent?
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Think about the relationship between the ranks.
Question 2.
If Rank(A) is 2 and Rank([A|b]) is 2, what can we say about the system?
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Check how ranks relate to solutions.
3Question 3.
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])
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Think about the equality between ranks.
4Question 4.
True or False: A system of linear equations can still be consistent if Rank(A) is less than Rank([A|b]).
- True
- False
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Recall the definition of consistency.
Question 5.
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.
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Calculate the ranks step by step.
Question 6.
Create a system of equations where Rank(A) < Rank([A|b]) and explain why no solutions exist geometrically.
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Visualize the equations on a graph.

4 more questions in this section. Enroll free to practise them all.