In P2 find the change-of-coordinatesB={1+t+t², 1-t+t², 2-2t+t²), C={ 1, t, t²}a.OOOaO1 1 21 -1 -2-2 12b.matrices from basis B to basis C.12 21 -1 -21 1 1C.1 1-3 -1 21 0 -1-1 00 2 -1

Given bases are: B=1+t+t2,1-t+t2,2-2t+t2C=1,t,t2 Write elements of B as linear combination of…

In P₂ find the change-of-coordinates B={1+t+t², 1-t+t², 2-2t+t²), C = { 1, t, t²) a. O a 1 1 2 1 -1 -2 2-2 1 + matrices from basis B to basis C. 12 2 b. 1 -1 -2 1 C. 0 2 0 -1 1 1 -3-1 1 1-3 1 1-1 0 0 2 -1

In P₂ find the change-of-coordinates B={1+t+t², 1-t+t², 2-2t+t²), C = { 1, t, t²) a. O a 1 1 2 1 -1 -2 2-2 1 + matrices from basis B to basis C. 12 2 b. 1 -1 -2 1 C. 0 2 0 -1 1 1 -3-1 1 1-3 1 1-1 0 0 2 -1

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.CR: Review Exercises

Problem 40CR

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Question

In P2 find the change-of-coordinates
B={1+t+t², 1-t+t², 2-2t+t²), C={ 1, t, t²}
a.
O
O
O
a
O
1 1 2
1 -1 -2
-2 1
2
b.
matrices from basis B to basis C.
12 2
1 -1 -2
1 1 1
C.
1 1
-3 -1 2
1 0 -1
-1 0
0 2 -1

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Step 1: Express elements of B as linear combination of elements of C.

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Step 2: Write the matrix of change of basis.

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