Consider a linear transformation T : <mi mathvariant="double-struck">R 3 <

Feinsn

Feinsn

Answered question

2022-06-17

Consider a linear transformation T : R 3 R 3 satisfying
T ( 1 2 3 ) = ( 4 5 6 )   and   T ( 2 3 4 ) = ( 5 6 7 ) .The question told me to find T ( 3 4 5 ) which I did but I am wondering how would I find the transformation matrix T?

Answer & Explanation

Arcatuert3u

Arcatuert3u

Beginner2022-06-18Added 30 answers

It amounts to finding a , b such that: a ( 1 2 3 ) + b ( 2 3 4 ) = ( 3 4 5 ) . Or:
( 1 1 1 ) = ( 2 3 4 ) ( 1 2 3 ) . This takes care of the question being asked.
To find T, we have to find: T ( e 1 ) , T ( e 2 ) , T ( e 3 ) by similar way.
kokoszzm

kokoszzm

Beginner2022-06-19Added 8 answers

Linearity give us T ( 1 1 1 ) = T ( 2 3 4 ) T ( 1 2 3 ) = ( 5 6 7 ) ( 4 5 6 ) = ( 1 1 1 ) Then T ( 3 4 5 ) = T ( 2 3 4 ) + T ( 1 1 1 ) = ( 5 6 7 ) + ( 1 1 1 ) = ( 6 7 8 ) In order to determine T completely we need the image of some basis B of R 3 under T.

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