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2 cards from this section. Quick, good the night before a test.
If vector v = (5, 2) is expressed in terms of basis B = {(1, 0), (0, 1)}, what is the coordinate vector?
Identify the coefficients based on the basis representation.
Express vector v = (3, 3) in terms of basis B = {(1, 1), (1, 0)}. What is the coordinate vector?
Think about how many times you need each basis vector.
What is a coordinate vector?
Think about representing vectors in terms of their basis.
True or False: All vectors in a vector space can be expressed in terms of the same basis.
Recall the properties of vector spaces and their bases.
Given basis B = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} and vector v = (5, 7, 2), compute and explain the coordinates of vector v.
Use the definition of coordinate vectors and linear combinations.
If we alter the basis to B' = {(2, 0), (0, 3)} and have vector v = (6, 9), find the coordinates of v in this new basis.
Express the vector in terms of the new basis and solve for the coefficients.
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