Practice Invertible Linear Transformations - 28.7 | 28. Linear Transformations | Mathematics (Civil Engineering -1)
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge

28.7 - Invertible Linear Transformations

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define an invertible linear transformation.

💡 Hint: Think about the ability to go back to the original state.

Question 2

Easy

What condition must the determinant of a matrix satisfy for the transformation to be invertible?

💡 Hint: Remember what a zero determinant indicates.

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 required for a linear transformation to be invertible?

  • The determinant must be zero
  • The determinant must be non-zero
  • The matrix must be square

💡 Hint: Consider what it means for a matrix to be singular.

Question 2

True or False: The identity transformation is a type of invertible linear transformation.

  • True
  • False

💡 Hint: Think about whether you can 'undo' the transformation.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given the matrix A = [[2, 3], [1, 4]], calculate \( \text{det}(A) \) and determine if A is invertible. If so, find the inverse matrix.

💡 Hint: Utilize the determinant formula and the matrix inversion method.

Question 2

Discuss a scenario in civil engineering where understanding invertibility of transformations is critical. Explain the implications of non-invertible transformations in that context.

💡 Hint: Consider the consequences of not being able to retrieve original forces from transformed ones.

Challenge and get performance evaluation