7. Consider the ordered bases S and T of R: ()} S = {81, 82, $3} and T = {t1, t2, t3} = We define a linear map L: R3 → R3 by setting L(s1) = $1 + 82, L(s2) = 81 + 83, and L(s3) = s2+ $3. (a) Find the matrix Pr-s = [Id]} of the basis change from S to T. (b) Find the matrix [L]g of L using the ordered basis S for the domain and range of the map. (c) Find the matrix [L] of L using the ordered basis T for the domain and range of the map.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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7. Consider the ordered bases S and T of R:
()}
S = {81, 82, $3}
and T = {t1, t2, t3} =
We define a linear map L: R3 → R3 by setting L(s1) = $1 + 82, L(s2) = 81 + 83, and L(s3) = s2+ $3.
(a) Find the matrix Pr-s = [Id]} of the basis change from S to T.
(b) Find the matrix [L]g of L using the ordered basis S for the domain and range of the map.
(c) Find the matrix [L] of L using the ordered basis T for the domain and
range
of the
map.
Transcribed Image Text:7. Consider the ordered bases S and T of R: ()} S = {81, 82, $3} and T = {t1, t2, t3} = We define a linear map L: R3 → R3 by setting L(s1) = $1 + 82, L(s2) = 81 + 83, and L(s3) = s2+ $3. (a) Find the matrix Pr-s = [Id]} of the basis change from S to T. (b) Find the matrix [L]g of L using the ordered basis S for the domain and range of the map. (c) Find the matrix [L] of L using the ordered basis T for the domain and range of the map.
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