a) Let T: R² R² be a linear transformation given by T(x, y)-(x+y,x-y). Find the matrix for T relative to the bases B = {(1,1),(1,0)} and B = {(1,0), (1, 2)}. b) Given the bases B-{(1, 1), (1,0)} and B-{(1,0), (1, 2)} of R², find the transition matrix from B to B'. c) Let T: R² R² be a linear transformation given by T(x, y) = (x + y, x - y). Given the bases B = {(1, 1), (1,0)} and B = {(1,0), (1, 2)} of R², compute [v], where v = (2,3).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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a)
Let T: R² R² be a linear transformation given by T(x, y) = (x+y,x-y).
Find the matrix for T relative to the bases B = {(1,1),(1,0)} and B' = {(1,0), (1, 2)}.
b)
Given the bases B-{(1, 1), (1,0)} and B-{(1,0), (1,2)} of R², find the transition matrix from B to B'.
c)
Let T: R² R² be a linear transformation given by T(x, y) = (x + y, x - y).
Given the bases B = {(1, 1), (1,0)} and B' = {(1,0), (1, 2)} of R²,
compute [v]B, where v = (2,3).
d)
Let T: R² R² be a linear transformation given by T(x, y) = (x + y,x-y).
Given the bases B = {(1, 1), (1,0)} and B' = {(1,0), (1, 2)} of R²,
compute [v], where v = (2, 3).
e)
Let T: R² R² be a linear transformation given by T(x, y) = (x+y,x-y).
Given the bases B = {(1, 1), (1,0)} and B' = {(1,0), (1, 2)} of R²,
compute [T(v)], where v = (2,3).
Transcribed Image Text:a) Let T: R² R² be a linear transformation given by T(x, y) = (x+y,x-y). Find the matrix for T relative to the bases B = {(1,1),(1,0)} and B' = {(1,0), (1, 2)}. b) Given the bases B-{(1, 1), (1,0)} and B-{(1,0), (1,2)} of R², find the transition matrix from B to B'. c) Let T: R² R² be a linear transformation given by T(x, y) = (x + y, x - y). Given the bases B = {(1, 1), (1,0)} and B' = {(1,0), (1, 2)} of R², compute [v]B, where v = (2,3). d) Let T: R² R² be a linear transformation given by T(x, y) = (x + y,x-y). Given the bases B = {(1, 1), (1,0)} and B' = {(1,0), (1, 2)} of R², compute [v], where v = (2, 3). e) Let T: R² R² be a linear transformation given by T(x, y) = (x+y,x-y). Given the bases B = {(1, 1), (1,0)} and B' = {(1,0), (1, 2)} of R², compute [T(v)], where v = (2,3).
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