Practice Conditions for Uniqueness of Solution - 25.4 | 25. Solutions of Linear Systems: Existence, Uniqueness, General Form | Mathematics (Civil Engineering -1)
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25.4 - Conditions for Uniqueness of Solution

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

True or False: A square matrix can have a unique solution.

💡 Hint: Think about the properties that could ensure a unique solution.

Question 2

Easy

Define full column rank in your own words.

💡 Hint: Consider how the rank relates to the number of columns.

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 condition must be satisfied for a linear system Ax = b to have a unique solution?

  • Rank(A) < n
  • Rank(A) = n
  • Rank(A) > n

💡 Hint: Consider the implications of having fewer or more equations than unknowns.

Question 2

True or False: A rectangular matrix can, in some cases, provide a unique solution.

  • True
  • False

💡 Hint: Think about how the matrix's rank relates to the system's variables.

Solve 2 more questions and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given the following augmented matrix: [[1, 2, 3, 5], [2, 4, 6, 10]], analyze its rank and determine if the system is consistent and whether it has a unique solution.

💡 Hint: Inspect the rows for linear dependency.

Question 2

For a system defined by a 4x4 matrix where three rows are linearly independent, determine what types of solutions are possible given three variables.

💡 Hint: Think about how many dimensions are represented versus how much freedom there is in choosing solutions.

Challenge and get performance evaluation