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},
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![BE THE LINEAR TRANSFORMATIONT: R³ → → P3(R), GIVEN BY T(x, y, z) = (x + y) + (v − z)t + (x+z)t² + (y=x+z)t³.
-⠀⠀⠀
IF [T]
=
2 1 0
-1 -1 -1
IS THE MATRIX OF T IN RELACTION TO THE BASES B =
2 2 2
2 0 1
CHOOSE AN OPTION
O a. B' = {1-t², −1+1²2², 2²2² +2²³, −1³3³},
b. B = {1-t, t+t², 1² + P²³₁ ²³},
O c. B = {1+t+t³₂ t + ²², −t+²²³ +2²³, -P³},
O d. B = {1-t+t², t + 2²₂ ²²³ +2²³, 2³}.
O e. B' = {1+t, t+1²₁ 1² + 1²³₁ −1³3³},
{(1, 1, 0), (0, 1, 1), (0, 0, -1)} OF R³ AND B' OF P3(R), THEN](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28444bb0-07f5-48bb-aa15-15291d4d4283%2Fc3028fc1-cfa8-4d2c-a64c-bdbb427e5f25%2Fdmntfsc_processed.png&w=3840&q=75)
Transcribed Image Text:BE THE LINEAR TRANSFORMATIONT: R³ → → P3(R), GIVEN BY T(x, y, z) = (x + y) + (v − z)t + (x+z)t² + (y=x+z)t³.
-⠀⠀⠀
IF [T]
=
2 1 0
-1 -1 -1
IS THE MATRIX OF T IN RELACTION TO THE BASES B =
2 2 2
2 0 1
CHOOSE AN OPTION
O a. B' = {1-t², −1+1²2², 2²2² +2²³, −1³3³},
b. B = {1-t, t+t², 1² + P²³₁ ²³},
O c. B = {1+t+t³₂ t + ²², −t+²²³ +2²³, -P³},
O d. B = {1-t+t², t + 2²₂ ²²³ +2²³, 2³}.
O e. B' = {1+t, t+1²₁ 1² + 1²³₁ −1³3³},
{(1, 1, 0), (0, 1, 1), (0, 0, -1)} OF R³ AND B' OF P3(R), THEN
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