Let L: R³ P2 be the linear transformation (no need to verify) defined by 3b 3c Let B₁ = b (2a-1/2-) = {(2,0,0), (1,0,2), (1, 1,-1) 1. Compute for [L]B L((a, b, c)) = (2a - x² + (6b+c)x+ (a+ 2 1 B₂ = {²+1,2x3,5x+4), B3 = {x²+1, x² + 2x - 2,7x + 1}.
Let L: R³ P2 be the linear transformation (no need to verify) defined by 3b 3c Let B₁ = b (2a-1/2-) = {(2,0,0), (1,0,2), (1, 1,-1) 1. Compute for [L]B L((a, b, c)) = (2a - x² + (6b+c)x+ (a+ 2 1 B₂ = {²+1,2x3,5x+4), B3 = {x²+1, x² + 2x - 2,7x + 1}.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 17CM
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![Let L: R³ P2 be the linear transformation (no need to verify) defined by
3b 3c
L((a, b, c)) = (2a -
2
-{(2,0,0), (1.0,2).
Let B₁ =
b
С
x² + (6b+c)x+ (a+
2
, (1, 0, 2), (1, 1,−1)}, 1 B₂ = {²+1,2x-3, 5x + 4), B3 = {x² +1, x² + 2x - 2,7x + 1}.
1. Compute for [L]B
2. Compute for the change of basis matrix from B₁ to B₂ and the change of basis matrix from B₂ to B₁.
Verify that they are inverses of each other.
3. Using the preceding items, find v if [L(v)] B₂
-0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08d8d8ab-e26a-4bca-a2e3-e0af75110088%2F465e5404-0453-417d-81b2-9b153bb5dc42%2Fmhwzvv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let L: R³ P2 be the linear transformation (no need to verify) defined by
3b 3c
L((a, b, c)) = (2a -
2
-{(2,0,0), (1.0,2).
Let B₁ =
b
С
x² + (6b+c)x+ (a+
2
, (1, 0, 2), (1, 1,−1)}, 1 B₂ = {²+1,2x-3, 5x + 4), B3 = {x² +1, x² + 2x - 2,7x + 1}.
1. Compute for [L]B
2. Compute for the change of basis matrix from B₁ to B₂ and the change of basis matrix from B₂ to B₁.
Verify that they are inverses of each other.
3. Using the preceding items, find v if [L(v)] B₂
-0
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