BE THE LINEAR TRANSFORMATIONT: R³ P3(R), GIVEN BY T(x, y, z) = (x + y) + (y −z)t + (x + z)t² + (y=x+z)t³. IF [T] = 2 1 0 -1 -1 -1 2 2 2 0 IS THE MATRIX OF T IN RELACTION TO THE BASES B = {(1, 1, 0), (0, 1, 1), (0, 0, -1)} OF R³ AND B OF P3(R), THEN 2 1 CHOOSE AN OPTION O a. B' = {1-², -1+R²₁ ²² +2²³₁ −B³}, O b. B = {1-t, t+ 2²₁ ²² +2³₁ ²³}, O c. B = {1+t+t³₁ 1+²²₂ −1+²²³ +2²³, -P}, O d. B = {1-t+t², 1+ ²²₁ ²² + ²³₂ ²³}. O e. B = {1+t, t+ P², P² + B³, − B³},
BE THE LINEAR TRANSFORMATIONT: R³ P3(R), GIVEN BY T(x, y, z) = (x + y) + (y −z)t + (x + z)t² + (y=x+z)t³. IF [T] = 2 1 0 -1 -1 -1 2 2 2 0 IS THE MATRIX OF T IN RELACTION TO THE BASES B = {(1, 1, 0), (0, 1, 1), (0, 0, -1)} OF R³ AND B OF P3(R), THEN 2 1 CHOOSE AN OPTION O a. B' = {1-², -1+R²₁ ²² +2²³₁ −B³}, O b. B = {1-t, t+ 2²₁ ²² +2³₁ ²³}, O c. B = {1+t+t³₁ 1+²²₂ −1+²²³ +2²³, -P}, O d. B = {1-t+t², 1+ ²²₁ ²² + ²³₂ ²³}. O e. B = {1+t, t+ P², P² + B³, − B³},
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.3: Matrices For Linear Transformations
Problem 43E: Let T:P2P3 be the linear transformation T(p)=xp. Find the matrix for T relative to the bases...
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