Consider the matrix transformation T : <mi mathvariant="double-struck">R 3

Jeramiah Campos

Jeramiah Campos

Answered question

2022-06-23

Consider the matrix transformation T : R 3 R 3 defined by
T ( x , y , z ) = ( 4 x + 3 y + z , 2 x 5 y , 6 y + 7 z ) .
Find the standard matrix for T, and use that matrix to find T ( 1 , 3 ) ..

Answer & Explanation

lorienoldf7

lorienoldf7

Beginner2022-06-24Added 19 answers

If you want to find T at a point ( x 0 , y 0 , z 0 ), then you simply perform the matrix multiplication
A ( x 0 y 0 z 0 ) = ( 4 3 1 2 5 0 0 6 7 ) ( x 0 y 0 z 0 ) .
For example:
T ( 1 , 3 , 4 ) = ( 4 3 1 2 5 0 0 6 7 ) ( 1 3 4 ) = ( 9 . . . . )

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