True/False: If $$ and $$ are both bases of the vector space $$, then the $$ matrix $$ sends vectors in $$-coordinates to the corresponding vectors in $$-coordinates.
True False
Consider two bases $$ and $$ for a vector space $$. Suppose that $$ and $$.
(a)
What is the $$ change-of-coordinates matrix $$?

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(b)
If $$ is a vector in $$-coordinates, what is the corresponding vector in $$-coordinates?

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(c)
What is the $$ change-of-coordinates matrix $$?
$$

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Consider two bases $$ and $$ for a vector space $$. Suppose that $$ and $$. Which change-of-coordinates matrix is $$?
$$ $$

Let $$ and $$ be bases for $$. Find both change-in-coordinates matrices.

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