[[-2,11],[4,2]] represents a linear transformation T:RR^2 to RR^2 with respect to the basis, [(3,1),(0,2)]. Find the matrix of T with respect to basis [(1,1),(−1,1)]

phepafalowl 2022-07-20 Answered
[ 2 11 4 2 ] represents a linear transformation T: R 2 to R 2 with respect to the basis, [(3,1),(0,2)]. Find the matrix of T with respect to basis [(1,1),(−1,1)]
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Answers (1)

Quenchingof
Answered 2022-07-21 Author has 14 answers
The change of basis matrix from ( ( 1 , 1 ) , ( 1 , 1 ) ) to ( ( 3 , 1 ) , ( 0 , 2 ) ) is
P = [ 1 3 1 3 1 3 2 3 ] .
So, the answer to your problem is the matrix
P 1 [ 2 11 4 2 ] P = [ 8 16 1 8 ] .

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