A adjust of works with matrix, likewise called a change matrix, states the transformation from one vector communication to another under a adjust of basis. For example, if

*
and also
*
room two vector bases in
*
, and also let
*
_B" /> it is in the works with of a vector
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in communication
*
and also
*
_(B^")" /> its works with in basis
*
.

You are watching: Find the change of coordinates matrix from b to c

Write the communication vectors

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and also
*
for
*
in collaborates relative to communication
*
as

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_B" />
*
*
" />

*
_B" />
*
*
." />

This way that

*
*
*

*
*
*

*
" />

which specifies the change of works with of a vector

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under the adjust of communication from
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come
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via


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