26.14 - Coordinate Systems and Change of Basis
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.
Practice Questions
Test your understanding with targeted questions
What is a basis in a vector space?
💡 Hint: Think about what building blocks are to a structure.
How do you express a vector in terms of a basis?
💡 Hint: It involves multiplication by coefficients.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is required to represent a vector in a different basis?
💡 Hint: Remember: responses depend on how bases relate.
True or False: Every vector can be uniquely represented by its coordinates in a chosen basis.
💡 Hint: Think about the definition of basis in vector spaces.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given two bases B = {(1,0), (0,1)} and C = {(1,1), (1,-1)}, determine the transformation matrix P and apply it to vector v = (2, 3).
💡 Hint: Work out P by solving the linear combinations for each basis.
If you have a vector that translates between two local and global coordinate systems, calculate the coordinates of the vector in the new system when provided with a transformation matrix.
💡 Hint: Focus on applying the matrix transformation as the first step.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.