Practice System of Linear Equations - 25.1 | 25. Solutions of Linear Systems: Existence, Uniqueness, General Form | Mathematics (Civil Engineering -1)
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25.1 - System of Linear Equations

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the general form of a system of linear equations?

💡 Hint: Think about the arrangement of equations and their variables.

Question 2

Easy

What does a homogeneous system mean?

💡 Hint: Recall that there's no constant on the right-hand side.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the matrix form of a system of linear equations?

  • Ax = b
  • Ax = 0
  • A + b = x

💡 Hint: Recall how we express our equations in one compact form.

Question 2

True or False: A system with Rank(A) < Rank([A∨b]) has infinitely many solutions.

  • True
  • False

💡 Hint: Think about what inconsistency means in terms of rank.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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.

Challenge and get performance evaluation