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2 cards from this section. Quick, good the night before a test.
What is a basis in a vector space?
Think about what building blocks are to a structure.
How do you express a vector in terms of a basis?
It involves multiplication by coefficients.
What is required to represent a vector in a different basis?
Remember: responses depend on how bases relate.
True or False: Every vector can be uniquely represented by its coordinates in a chosen basis.
Think about the definition of basis in vector spaces.
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).
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.
Focus on applying the matrix transformation as the first step.
5 more questions in this section. Enroll free to practise them all.
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